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Equation Word Problems Worksheets

This compilation of a meticulously drafted equation word problems worksheets is designed to get students to write and solve a variety of one-step, two-step and multi-step equations that involve integers, fractions, and decimals. These worksheets are best suited for students in grade 6 through high school. Click on the 'Free' icons to sample our handouts.

One Step Equation Word Problem Worksheets

One Step Equation Word Problem Worksheets

Read and solve this series of word problems that involve one-step equations. Apply basic operations to find the value of unknowns.

(15 Worksheets)

Two-Step Equation Word Problems: Integers

Two-Step Equation Word Problems: Integers

Interpret this set of word problems that require two-step operations to solve the equations. Each printable worksheet has five word problems ideal for 6th grade, 7th grade, and 8th grade students.

  • Download the set

Multi-Step Equation Word Problems: Integers

Multi-Step Equation Word Problems: Integers

Read each multi-step word problem in these high school pdf worksheets and set up the equation. Solve and find the value of the unknown. More than two steps are required to solve the problems.

Two-Step Equation Word Problems: Fractions and Decimals

Two-Step Equation Word Problems: Fractions and Decimals

Read each word problem and set up the two-step equation. Solve the equation and find the solution. This selection of worksheets includes both fractions and decimals.

Multi-Step Equation Word Problems: Fractions and Decimals

Multi-Step Equation Word Problems: Fractions and Decimals

Write multi-step equations that involve both fractions and decimals based on the word problems provided here. Validate your responses with our answer keys.

MCQ - Equation Word Problems

MCQ - Equation Word Problems

Pick the correct two-step equation that best matches word problems presented here. Evaluate the ability of students to solve two-step equations with this array of MCQ worksheets.

Related Worksheets

» One-Step Equation

» Two-Step Equation

» Multi-Step Equation

» Algebraic Identities

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Solving inequalities worksheets.

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Inequalities Worksheets

Are you looking for free math worksheets that will help your students develop and master real-life math skills?  The algebra worksheets below will introduce your students to solving inequalities and graphing inequalities.  As they take a step-by-step approach to solving inequalities, they will also practice other essential algebra skills like using inverse operations to solve equations.

Solving Inequalities Worksheet 1 – Here is a twelve problem worksheet featuring simple one-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 1 RTF Solving Inequalities Worksheet 1 PDF Preview Solving Inequalities Worksheet 1  in Your Browser View Answers 

Solving Inequalities Worksheet 2 – Here is a twelve problem worksheet featuring simple one-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 2 RTF Solving Inequalities Worksheet 2 PDF Preview Solving Inequalities Worksheet 2 in Your Browser View Answers

Solving Inequalities Worksheet 3 – Here is a twelve problem worksheet featuring two-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 3 RTF Solving Inequalities Worksheet 3 PDF Preview Solving Inequalities Worksheet 3 in Your Browser View Answers

Solving Inequalities Worksheet 4 – Here is a twelve problem worksheet featuring one-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 4 RTF Solving Inequalities Worksheet 4 PDF Preview Solving Inequalities Worksheet 4 in Your Browser View Answers

Solving Inequalities Worksheet 5 – Here is a twelve problem worksheet featuring two-step inequalities.  Use inverse operations or mental math to solve for x . Solving Inequalities Worksheet 5 RTF Solving Inequalities Worksheet 5 PDF Preview Solving Inequalities Worksheet 5 in Your Browser View Answers

Graphing Inequalities Workheet 1 –  Here is a 15 problem worksheet where students will graph simple inequalities like  “ x < -2″  on a number line. Graphing Inequalities Worksheet 1 RTF Graphing Inequalities 1 PDF View Answers

Graphing Inequalities Workheet  2 –  Here is a 15 problem worksheet where students will graph simple inequalities like  “ x < -2″  and “ -x > 2″  on a number line.  Be careful, you may have to reverse one or two of the inequality symbols to get the correct solution set. Graphing Inequalities 2 RTF Graphing Inequalities 2 PDF View Answers

Graphing Inequalities Workheet  3 –  Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features one-step addition inequalities such as   “x + 5 > 7”. Graphing Inequalities 3 RTF Graphing Inequalities 3 PDF View Answers

Graphing Inequalities Workheet  4 –  Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features one-step addition and subtraction inequalities such as   “5 + x > 7”  and  “x – 3″ < 21”. Graphing Inequalities 4 RTF Graphing Inequalities 4 PDF View Answers

Graphing Inequalities Workheet  5 –   Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features two-step addition inequalities such as   “2x + 5 > 15” . Graphing Inequalities 5 RTF Graphing Inequalities 5 PDF View Answers

Graphing Inequalities Workheet  6 –  Here is a 12 problem worksheet where students will both  solve  inequalities and  graph  inequalities on a number line.  This set features two-step addition and subtraction inequalities such as   “2x + 5 > 15”  and “ 4x -2 = 14. Graphing Inequalities 6 RTF Graphing Inequalities 6 PDF View Answers

Absolute Value Inequality Worksheets (Single Variable)

Absolute Value Inequality Worksheet 1 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.  These are one-step inequalities with mostly positive integers. Absolute Value Equations Worksheet 1 RTF Absolute Value Equations Worksheet 1 PDF View Answers

Absolute Value Inequality Worksheet 2 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.   These are one-step inequalities where you’ll need to use all of your inverse operations knowledge. Absolute Value Equations Worksheet 2 RTF Absolute Value Equations Worksheet 2 PDF View Answers

Absolute Value Inequality Worksheet 3 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.  These are two-step inequalities where you’ll need to use all of your inverse operations knowledge. Absolute Value Equations Worksheet 3 RTF Absolute Value Equations Worksheet 3 PDF View Answers

Absolute Value Inequality Worksheet 4 –  Here is a 9 problem worksheet where you will find the solution set of absolute value inequalities.  These are two-step inequalities that can get quite complicated.  A nice challenge for your higher-level learners. Absolute Value Equations Worksheet 4 RTF Absolute Value Equations Worksheet 4 PDF View Answers

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20 Comments

This web is good

Thanks for your support.

i like it. Its very helpful.

I appreciate the feedback. Good luck with your math endeavors!

I like this website. It is very helpful for students.

Thanks. I’ll be adding more worksheets soon.

Interesting questions. Very good.

Thanks. I’m glad you enjoyed them.

This is a great site! Thanks so much for helping me teach this concept to my 5th graders!

Mr. Colwell

I’m glad that I could help. Thanks for visiting the site and come back often!

Kaity Fanara

Very helpful, thanks!

You’re very welcome. I plan to add some Graphing Inequalities Worksheets soon. Thanks for your support.

c’moon! so easy give me something like, ( m-2 ) x2 – (m+5) x + m-8 = 0, if it has 2 equal roots, what’s m? i need this kind, where can i find

That’s a pretty good one. Let me see what I can do.

Mr. Lindugani Mlilile

Thanks for your website which helps me teach my students of form one in Tanzania. I always teach my students on how solve the topic of inequality. Please add more topic so that my students will continue to enjoys!

It’s nice to hear from our international visitors. I’m always adding new content. Check back often!

It is helpful but I can’t see the answer sheet for all of them.

wish their was some fractions inequalities and equalities

however work sheets have helped me tremendously just the one little flaw of not having fraction problems.

I LOVE THIS WEBSITE. I USE IT EVERY DAY TO STUDY FOR TEST OR QUIZ FOR SCHOOL.

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Algebra and Pre-Algebra

Up

Word problems

Sometimes systems of equations can be used to model word problems.  Let’s jump straight to an example.

Example:   The school that Matt goes to is selling tickets to a choral performance.  On the first day of ticket sales the school sold 12 adult tickets and 3 student tickets for a total of $129.  The school took in $104 on the second day by selling 2 adult tickets and 6 student tickets.  Find the price of an adult ticket and the price of a student ticket.

Solution:   Let a be the price of an adult ticket, and let s represent the price of a student ticket.  On the first day of the performance the 12 adult tickets were sold at the price of a and 3 student tickets were sold at the price of s .  The sum of their sales was $129.  We can model this by

\(12a + 3s = 129\)

Using a similar reasoning, we can model the second day of sales by

\(2a + 6s = 104\)

Combining these two equations gives us a system that we can solve!  We use elimination:

\(12a + 3s = 129\) \(2a + 6s = 104\)

\( - 24a - 6s =  - 258\) \(2a + 6s = 104\)

\( - 22a =  - 154\)

That is, an adult ticket cost $7.  Then by substituting \(a = 7\) into the second equation, we have

\(2a + 6s = 104\) \(2\left( 7 \right) + 6s = 104\) \(14 + 6s = 104\) \(6s = 90\) \(s = 15\)

That is, a student ticket costs $15.

Another Example:   The senior class at High School A and High School B planned separate trips to the water park.  The senior class at High School A rented and filled 8 vans and 4 buses with 256 students.  High School B rented and filled 4 vans and 6 buses with 312 students.  Each van and each bus carried the same number of students.  How many students can a van carry?  How many students can a bus carry?

Solution:   Let v be the number of students a van can carry.  Let b be the number of students a bus can carry.  High School A’s situation can be modeled by

\(8v + 4b = 256\)

Similarly, High School B’s situation can be modeled by

\(4v + 6b = 312\)

We solve the system using elimination

\(8v + 4b = 256\) \(4v + 6b = 312\)

\(8v + 4b = 256\) \( - 8v - 12b =  - 624\)

\( - 8b =  - 368\)

That is, a bus can hold 46 students.  Substituting 46 into the first equation gives

\(8v + 4b = 256\) \(8v + 4\left( {46} \right) = 256\) \(8v + 184 = 256\) \(8v = 72\) \(v = 9\)

That is, each van can hold 9 students.

Below you can   download   some   free   math worksheets and practice.

COM_PHOCADOWNLOAD_HOT

This free worksheet contains 10 assignments each with 24 questions with answers. Example of one question:

Systems-of-Equations-and-Inequalities-Word-problems-easy

Watch below how to solve this example:

Systems-of-Equations-and-Inequalities-Word-problems-medium

Systems-of-Equations-and-Inequalities-Word-problems-hard

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Equations and Inequalities Word Problems Worksheets

Inequalities are mathematically comparisons of values as where equations are all about displaying equality. Equations are math statements that shows two equal expressions. Inequalities state that one side of the math statement is larger or smaller than the other. These worksheets and lessons teach students how to write equations and inequalities that are based on word problems. This will empower your students to solve much more complex problem types that will require critical thinking skills that they should be ready for at the high school level. The goal is for them to be able to read these word problems and represent them with mathematical statements of their own.

Aligned Standard: HSA-CED.A.3

  • Simple Equations Step-by-step Lesson - Who ever knew that picking a dance class could be such a mathematically dilemma?
  • Guided Lesson - The problems are a bit lengthy to help you work with student and teach them to outline.
  • Guided Lesson Explanation - Graphing them really helps bring the answers to you quickly.
  • Practice Worksheet - I found these to be some of the most difficulty word problems to write in my life. To vary all the scenarios is quite difficult.
  • Matching Worksheet - Match every heavy worded problem to it's output.
  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

This section took me forever to write. I just kept running out of ideas.

  • Homework 1 - Jian wants to take part in a Taekwondo class. He has two choices. Taekwondo class A costs $10 per month and $100 as registration fees.
  • Homework 2 - Wilson is planning to open a Yoga studio. He has to pay $30 as rent for the studio and $5 per member for utilities. Each member will pay $15 for the yoga class.
  • Homework 3 - George makes an average 15 baskets per game and made 40 baskets so far. Shane makes an average 10 baskets per game and made 55 baskets so far. If their averages remain the same, how many games do they have to play in order to score the same number of baskets?

Practice Worksheets

A big thanks to all my past colleagues that throw ideas at me to come up with new problems on this one.

  • Practice 1 - Daniel has an office. He has to pay $20 a day in rent for the office and $2 per hour for parking. He pays $30 each day. How many hours does Daniel park his car?
  • Practice 2 - Emma organized a party in a club. She has to pay $200 to an event organizer and her expenses for dinner are $10 per person. Each person pays $15 to Emma. How many people does Emma need to come to the party to reach a breakeven point?
  • Practice 3 - Eva wants to print copies of her notes in hardcover book format. She has two choices. Printing A costs a setup fee of $40 and $3 for every book. Printing B costs a setup fee of $30 and $4 for every book. Find out when the two options cost the same amount. How many books is that?

Math Skill Quizzes

This can be a challenging task for many students.

  • Quiz 1 - Two road crews are paving a straight section of road. The first crew has completed paving 12 miles and is completing 2 additional miles per day. The second crew has finished 8 miles and is completing 3 miles per day. How long will it take for both teams to cover the same number of miles?
  • Quiz 2 - Vijay was renting a skateboard for his competition training. Skateboard A is $12 per month and requires a down payment of $100. Skateboard B is $15 per month rent and requires a down payment of $80. How many months would Vijay need to rent the skateboard in order for the total cost to be same?
  • Quiz 3 - Marlin and Watson are playing video games. Marlin has 40 points and is earning 5 points every turn. Watson has 50 points and is earning 3 points every turn. In a certain number of turns, the score will be tied. How many points will they each have?

How to Write a System of Equations

When you are solving real-world algebraic equations, you can get easily confused. Considering that such problems are complex to solve and are known as the system of equations. Let us consider an example to learn its concept quickly. David spent $131 one pair of shoes, since one pair of sneakers had a price of $15, while the slippers had a cost of $28. In total, he bought 7 pairs of shoes. How many pairs of each shoe did he buy of each type?

In this section, we are only learning how to write the system of equations and not solve them. In this problem, we have to write two equations, given that there are two variables. The two variables are the two pairs of shoes, i.e., the sneakers and the slippers. Let us consider the two variables like x and y. Now, in total, David bought 7 pairs of shoes comprising of the two variables. So, the first equation becomes:

[1] => x + y = 7

The first equation depicts the number of shoes bought by David. The second equation will illustrate the total money he spent. He spent a total of $131 comprising of $15 worth of x’s and $28 worth of y’s. So, the equation becomes:

[2] => 15x + 28y = 7

Now, you have two equations that you need to simultaneously solve to find out how many pairs did David bought for each type of shoes.

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Writing Inequalities from Word Problems

Learn about writing inequalities from word problems with help from our practice examples. If you want to test yourself, or get some practice, then try one of our graded worksheets, or our online quiz.

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What is an Inequality?

The language of inequalities.

  • How to Write an Inequality from a Word Problem
  • Write an Inequality from a Word Problems Examples

Writing Inequalities from Word Problems Worksheets

  • Writing Inequalities from Word Problems Online Quiz
  • More related resources

An inequality is when you have a relationship between two values of expressions which are not equal to each other.

There are a few different options for different types of inequalities:

  • Greater than (>) where one expression or value is greater than another, e.g. 7 > 5
  • Less than (<) where one expression or value is less than another, e.g. 9 < 2 x 6
  • Greater than or equal to (≥) where one expression or value is greater than or equal to another, e.g. 20 + 4 ≥ 17
  • Less than or equal to (≤) where one expression or value is less than or equal to another, e.g. 18 ≤ 9 x 2
  • Not equal to (≠) where one expression or value is not equal to another, e.g. 7 ≠ 4

When writing inequalities from word problems, we have to look carefully at and understand the language being used.

Different words and phrases have different meanings when deciding on which inequality to use.

The mathematical notation is really just a shorthand way of writing the words more efficiently and clearly.

Here is a quick table showing some of the written expressions often used and which inequality they are represented by.

Note: the word 'between' is mainly used to mean between inclusively (including end points).

However, sometimes 'between' is used to mean between exclusively (excluding end points).

To avoid ambiguity, it is good practice to include the word 'inclusive' or 'exclusive' to make it completely clear if the end points are included or not.

Some simple examples showing inequalities from phrases:

The variable names (letters) have been chosen at random - you can use any variable name to represent any value.

Note: you need to read the word problem carefully because sometimes the inequality does not match the language used, especially when the inequality involves finding out what is left over or what remains after an amount is taken away. See Examples 2) and 7) below.

How to Write Inequalities from Word Problems

When we are writing an inequality from a word problem, we are basically translating the word problem into mathematical language and symbols.

When writing an inequality from a word problem, there are two simple steps you need to follow...

Step 1) Read the word problem carefully and change the word problem into algebra.

  • use the language of inequalities table to help you select the right inequality

Step 2) Use algebra to solve the word problem

Step 3) rewrite the inequality using algebra., write an inequality from a word problem examples.

The best way to learn how to write inequalities from word problems and see how they work is to look at some ready made examples.

Writing Inequalities from Word Problems - Basic Examples

Here are some examples of writing inequalities from word problems.

Example 1) Sally bakes some cookies and needs to put them in the over for at least 12 minutes. Write an inequality using the variable t to show how long the cookies need to be baked in the oven.

The vocabulary which tells us about the inequality are the words: at least .

This means we need to use the ≥ symbol.

So the inequality is t ≥ 12 minutes

Example 2) Newton has a 30 ounce bottle of water. He drinks over half of the bottle. Write an inequality using the variable c to show how many ounces are left in the bottle.

The vocabulary which tells us about the inequality are the words: over .

However, because he has drunk over half the bottle, it means that there is under half a bottle left.

So the symbol we need is < and the amount is ½ of 30 = 15.

So the inequality is b < 15 ounces

Example 3) Anna is more than three times as old as Bertie. If Bertie is 8 years old, write an inequality using the variable A to show how old Anna is.

The vocabulary which tells us about the inequality are the words: more than .

So the symbol we need is > and the amount is 3 x 8 = 24.

So the inequality is A > 24 years old

Example 4) A book has 14 chapters.The shortest chapter has 12 pages. Write an inequality using the variable p to show how many pages the book has.

The vocabulary which tells us about the inequality are the words: shortest .

If the shortest chapter has 11 pages, then there must be some chapters with more than 11 pages.

So the symbol we need is > and the amount is 14 x 12 = 168.

So the inequality is p > 168 pages.

Writing Inequalities from Word Problems -Intermediate Examples

These examples use two different variables and express one variable in terms of another.

Example 5) Captain and Frazer have some gold coins. Captain has at least three times as many coins as Frazer. Write an inequality for the number of coins Captain has (c) in terms of the number of coins Frazer has (f).

So the symbol we need is ≥

So the inequality is c ≥ 3f.

Example 6) In a hotel there are f flights of stairs. Each flight has a maximum of 12 steps. There are also 3 steps up to the main entrance. Write an expression for the total number of steps, s, in terms of f.

The vocabulary which tells us about the inequality are the words: a maximum of .

So the symbol we need is ≤

We know that there are f flights of steps and also 3 extra steps.

So the inequality is s ≤ 12f + 3.

Writing Inequalities from Word Problems - Harder Examples

These examples involve solving word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.

There are also examples where the variable lies between two values.

Example 7) Captain has a one-liter bottle of water. He drinks more than one-quarter of the bottle but less than one-half of the bottle. Write an inequality using the variable b to show the amount of water than is left in the bottle.

The vocabulary which tells us about the inequality are the words: more than and less than .

However, because we are looking at what is left in the bottle, rather than what has been drunk, we need to think carefully about the inequalities!

He drinks more than one-quarter of the bottle, so there will be less than three-quarters of the bottle left, so we need the symbol <

He drinks less than one-half of the bottle, so there will be one-half or more of the bottle left, so we need the symbol ≥

Half of the bottle = ½ liters = 500 ml. 1000 - 500 = 500 ml

Quarter of the bottle = ¼ liters = 250 ml. 1000 - 250 = 750 ml

So the inequality is b ≥ 500 ml and b < 750 ml This can be simplified to: 500 ≤ b < 750 ml This means that he has at least 500 ml but less than 750 ml left.

Example 8) Captain has challenged himself to catch a minimum of 50 fish from a lake. He manages to catch 8 of them and put them in his bucket. If he catches 6 fish every hour, write an inequality to show the time (t) in hours it will take him to reach his target.

The vocabulary which tells us about the inequality are the words: a minimum of .

The inequality we get from this problem is 6t + 8 ≥ 50

We are not finished yet, because this needs to be simplified and written in terms of t.

6t + 8 ≥ 50 so 6t ≥ 42

If we divide both sides of this inequality by 6, we get:

So the inequality is t ≥ 7 hours He needs to fish for at least 7 hours to reach his target.

Example 9) It takes Newton between 23 and 28 seconds (inclusive) to swim a length of a swimming pool. Write an inequality using the variable t to show how long it will take him to swim 3 lengths.

The vocabulary which tells us about the inequality are the words: between (inclusive) .

So the symbol we need is ≤ and ≥

3 x 23 = 69 and 3 x 28 = 84

So the inequality is t ≥ 69 and t ≤ 84 This can be simplified to: 69 ≤ t ≤ 84 It will take him between 69 and 84 seconds (inclusive) to swim 3 lengths.

We have a range of different inequality worksheets which involve writing inequalities from a range of word problems..

We have split the sheets into 3 sections: A, B and C

  • Section A involves basic level questions aimed at 6th grade
  • Section B involves medium level questions aimed at 6th and 7th grade
  • Section C involves more advanced questions aimed at 7th and 8th grade

Writing Inequalities from Word Problems - Section A Easier

Sheet 1 involves picking the vocabulary and relevant information from the problem and writing the inequality

Sheet 2 involves the same skills as Sheet 1, but also involves an arithmetic operation to get the inequality.

  • Inequalities from Word Problems Sheet A1
  • PDF version
  • Inequalities from Word Problems Sheet A2

Writing Inequalities from Word Problems - Section B Medium

Sheet 1 involves using two variables and writing an inequality for one variable in terms of the other variable

Sheet 2 is similar to Sheet 1 but with slightly harder problems.

  • Inequalities from Word Problems Sheet B1
  • Inequalities from Word Problems Sheet B2

Writing Inequalities from Word Problems - Section C

Sheet 1 involves using one variables and using the information to solve the inequality, usually in the form px + q > r or px + q < r, where p, q, and r are specific rational numbers

Sheet 2 involves the same skills as Sheet 1 but has compound inequalities in each question

  • Inequalities from Word Problems Sheet C1
  • Inequalities from Word Problems Sheet C2

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

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6th Grade Ratio and Unit Rate Worksheets

These 5th grade ratio worksheets are a great way to introduce this concept.

We have a range of part to part ratio worksheets and slightly harder problem solving worksheets.

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  • Unit Rate Problems 6th Grade

6th Grade Algebra Worksheets

If you are looking for some 6th grade algebra worksheets to use with your child to help them understand simple equations then try our selection of basic algebra worksheets.

There are a range of 6th grade math worksheets covering the following concepts:

  • Generate the algebra - and write your own algebraic expressions;
  • Calculate the algebra - work out the value of different expressions;
  • Solve the algebra - find the value of the term in the equation.
  • Use the distributive property to factorize and expand different expressions
  • 6th Grade Distributive Property Worksheets
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  • Basic Algebra Worksheets (6th & 7th Grade)

Writing Inequalities from Word Problems Quiz

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This quick quiz tests your skill at writing inequalities from a range of word problems.

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Solving Inequality Word Questions

(You might like to read Introduction to Inequalities and Solving Inequalities first.)

In Algebra we have "inequality" questions like:

soccer teams

Sam and Alex play in the same soccer team. Last Saturday Alex scored 3 more goals than Sam, but together they scored less than 9 goals. What are the possible number of goals Alex scored?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

  • Read the whole thing first
  • Do a sketch if needed
  • Assign letters for the values
  • Find or work out formulas

We should also write down what is actually being asked for , so we know where we are going and when we have arrived!

The best way to learn this is by example, so let's try our first example:

Assign Letters:

  • the number of goals Alex scored: A
  • the number of goals Sam scored: S

We know that Alex scored 3 more goals than Sam did, so: A = S + 3

And we know that together they scored less than 9 goals: S + A < 9

We are being asked for how many goals Alex might have scored: A

Sam scored less than 3 goals, which means that Sam could have scored 0, 1 or 2 goals.

Alex scored 3 more goals than Sam did, so Alex could have scored 3, 4, or 5 goals .

  • When S = 0, then A = 3 and S + A = 3, and 3 < 9 is correct
  • When S = 1, then A = 4 and S + A = 5, and 5 < 9 is correct
  • When S = 2, then A = 5 and S + A = 7, and 7 < 9 is correct
  • (But when S = 3, then A = 6 and S + A = 9, and 9 < 9 is incorrect)

Lots More Examples!

pups

Example: Of 8 pups, there are more girls than boys. How many girl pups could there be?

  • the number of girls: g
  • the number of boys: b

We know that there are 8 pups, so: g + b = 8, which can be rearranged to

We also know there are more girls than boys, so:

We are being asked for the number of girl pups: g

So there could be 5, 6, 7 or 8 girl pups.

Could there be 8 girl pups? Then there would be no boys at all, and the question isn't clear on that point (sometimes questions are like that).

  • When g = 8, then b = 0 and g > b is correct (but is b = 0 allowed?)
  • When g = 7, then b = 1 and g > b is correct
  • When g = 6, then b = 2 and g > b is correct
  • When g = 5, then b = 3 and g > b is correct
  • (But if g = 4, then b = 4 and g > b is incorrect)

A speedy example:

bike

Example: Joe enters a race where he has to cycle and run. He cycles a distance of 25 km, and then runs for 20 km. His average running speed is half of his average cycling speed. Joe completes the race in less than 2½ hours, what can we say about his average speeds?

  • Average running speed: s
  • So average cycling speed: 2s
  • Speed = Distance Time
  • Which can be rearranged to: Time = Distance Speed

We are being asked for his average speeds: s and 2s

The race is divided into two parts:

  • Distance = 25 km
  • Average speed = 2s km/h
  • So Time = Distance Average Speed = 25 2s hours
  • Distance = 20 km
  • Average speed = s km/h
  • So Time = Distance Average Speed = 20 s hours

Joe completes the race in less than 2½ hours

  • The total time < 2½
  • 25 2s + 20 s < 2½

So his average speed running is greater than 13 km/h and his average speed cycling is greater than 26 km/h

In this example we get to use two inequalities at once:

ball throw

Example: The velocity v m/s of a ball thrown directly up in the air is given by v = 20 − 10t , where t is the time in seconds. At what times will the velocity be between 10 m/s and 15 m/s?

  • velocity in m/s: v
  • the time in seconds: t
  • v = 20 − 10t

We are being asked for the time t when v is between 5 and 15 m/s:

So the velocity is between 10 m/s and 15 m/s between 0.5 and 1 second after.

And a reasonably hard example to finish with:

Example: A rectangular room fits at least 7 tables that each have 1 square meter of surface area. The perimeter of the room is 16 m. What could the width and length of the room be?

Make a sketch: we don't know the size of the tables, only their area, they may fit perfectly or not!

  • the length of the room: L
  • the width of the room: W

The formula for the perimeter is 2(W + L) , and we know it is 16 m

  • 2(W + L) = 16
  • L = 8 − W

We also know the area of a rectangle is the width times the length: Area = W × L

And the area must be greater than or equal to 7:

  • W × L ≥ 7

We are being asked for the possible values of W and L

Let's solve:

So the width must be between 1 m and 7 m (inclusive) and the length is 8−width .

  • Say W = 1, then L = 8−1 = 7, and A = 1 x 7 = 7 m 2 (fits exactly 7 tables)
  • Say W = 0.9 (less than 1), then L = 7.1, and A = 0.9 x 7.1 = 6.39 m 2 (7 won't fit)
  • Say W = 1.1 (just above 1), then L = 6.9, and A = 1.1 x 6.9 = 7.59 m 2 (7 fit easily)
  • Likewise for W around 7 m

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Free Linear Inequalities Word Problems Worksheet

While teaching high school, one of the biggest struggles I have seen students face is applying math concepts to the real-world. This is true when it comes to solving linear inequalities word problems too. Students often find it challenging to grasp how these mathematical principles translate into practical, everyday life scenarios.

That’s why I have put together this linear inequalities word problems worksheet! My goal is to help you learn a few tips and tricks and practice applying linear inequalities to the real-world! 

What are Linear Inequality Word Problems?

Lesson plans that focus on linear inequality word problems typically show students how to apply the skills they developed while solving inequalities to the real-world. There are a wide variety of inequality applications, ranging from social studies to physical science. Regardless of the application, the idea is that you will be faced with a word problem that requires you to model the scenario using a linear inequality.

In general, linear inequality word problems describe how one quantity has to be less than or greater than another. Your goal is then to use inequality symbols and  algebraic expressions  to represent the scenario algebraically.

For most, the concept of a linear inequality is first introduced in middle school (although this will vary by curriculum). My daughter, for example, is in 2nd grade math and is just starting to explore these problems. Others may not see this concept until later in high school (in some cases not until the 12th grade).

How to Solve a Linear Inequality Word Problem

The best way to solve any math word problem is to start by reading the question very carefully, and linear inequality word problems are no different!

I always encourage my students to underline or highlight any key words and important information. When it comes to how to solve a linear inequality word problem, the key words usually help you understand:

  • which quantities you are working with
  • whether you are working with  less than  or  greater than symbols

list of inequality symbols

Once you have identified this important information, your goal is to write an algebraic expression using an inequality symbol that models the scenario. You can then solve the inequality using a similar process to what you would apply when solving one-step equations or  two step equations .

There are many different ways to represent the solution to an inequality problem. Sometimes you will be asked to use a number line, which shows all the negative values or positive values that belong to a solution set. The worksheet attached below will provide you with some practice using number lines to communicate your answers to inequality word problems.

​Solving a Linear Inequality Word Problem Example

Age problems are common applications that you will see when solving linear inequality word problems. These types of problems can be simple or complex, but I wanted to start by sharing a simple one here so that you can understand the basics of how to solve linear inequality word problems.

A father is 3 times as old as his son, but three times his son’s age is less than 30. What is the oldest the son can be?

We can begin by calling out the key words that give us important information. In this case, the following two pieces of information are considered important to the problem:

  • “3 times as old as”
  • “less than 30”

This tells us that we will be working with a “<” symbol, and multiplication of a quantity by 3. If we let  n  represent the age of the son, we can set up a linear inequality as follows:

$$3n<30$$

Reading this statement in English tells us that “3 times the son’s age is less than 30”. If you head back to the original problem, that seems to match the scenario given, doesn’t it? Great! That tells us that we have a good algebraic model for our real-world problem! Let’s move on and start solving!

Remember that we can solve a linear inequality using algebra in a similar way to solving a linear equation. This means that we can add or subtract terms on both sides of the inequality symbol, and we can also multiply and divide terms on both sides of the inequality symbol.

In this case, since we are multiplying  n  by 3, we divide both sides by 3 to isolate  n.

$$\frac{3n}{3}< \frac{30}{3}$$

$$n<10$$

This tells us that the son’s age must be less than 10 in order for the father to be three times his age but still less than 30 years old himself.

We can test this by multiplying a number greater than 10 by 3. For example, \(11 \times 3 = 33\). Notice that 33 is  not  less than 30. Therefore the son cannot be 11. The only values that will make this inequality statement true are values that are less than (not including) 10.

We can represent this solution on a number line by placing a hollow circle at 10 and drawing an arrow to the left toward the negative values. However, we should stop at zero since the son’s age cannot be less than zero. Note that the son must also not be equal to zero. If he were, the father would be \(3 \times 0 = 0\) as well!

a number line representing the solution 0 < x

If you need more practice with the algebra strategies that can be used to solve inequalities, check out this collection of  solving linear inequalities worksheets .

Linear Inequalities Word Problems Worksheet

Now that you have had some practice applying your understanding of linear inequalities to solve a real-world problem, you are ready to practice! Below I have included a linear inequalities word problem worksheet that covers a variety of problem types, ranging from age problems, to a bake sale problem with pink cupcakes!

As promised, this worksheet will also provide you with practice representing the solution to a linear inequality word problem on a number line. While you should be sure to attempt every problem as independent work first, make sure that you also check the answer key! This is an important step to make sure that you fully understand each problem.

My hope is that you find this linear inequalities word problems worksheet helpful as independent work whether you are in 1st grade math, 7th grade math, or anything in between!

Download the PDF worksheet by clicking below!

Practice Solving Linear Inequalities Word Problems

I hope this linear inequalities word problems worksheet has provided you with some practice with applying this important math concept to the real-world! My goal was to share examples that cover a variety of areas of life. Hopefully solving these problems also gave you an appreciation for how linear inequalities can be used in everyday life.

Whether you first learned about linear inequality word problems in the 6th grade or are just experiencing them for the first time in the 12th grade, the most important thing you can do is practice. Solving many different types of linear inequalities word problems will help you start to recognize patterns. This will help you with the first initial step of writing the inequality as an algebraic statement, something many students find challenging! 

With consistent practice, you’ll develop a strong foundation in solving linear inequalities, enhancing your problem-solving skills and confidence in applying mathematical concepts to diverse real-world scenarios. Keep exploring and practicing, and you’ll find that handling linear inequalities becomes more intuitive over time!

If you are looking for more word problem resources, check out this linear equations word problems worksheet !

Did you find this linear inequalities word problems worksheet helpful? Share this post and subscribe to Math By The Pixel on YouTube for more helpful mathematics content!

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Inequalities Worksheets

The worksheets given here require students to solve inequalities in the regular way and also on the number line. Some of the questions ask you to find the inequality variables’ values.

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Equations and Inequalities Worksheets

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. An equation is a statement that asserts the equality of two expressions and a linear inequality is an inequality which involves a linear function. It shows the data which is not equal in graph form.

Equations and inequalities worksheets provide questions based on the concept and both have equations or inequalities that contain at least one variable and are known as open sentences.

Benefits of Equations and Inequalities Worksheets

Equations and inequalities is an essential concept in mathematics. Solving equations and inequality worksheets is helpful as they are used to compare numbers and determine the range or ranges of values that satisfy the conditions of a given variable. Equations and inequalities can be represented on a number line.

Linear inequalities are used in real life to maximize a profit or as complicated as determining the correct combination of drugs to give a patient.

Download Equations and Inequalities Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

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Inequalities Word Problems Worksheet

Related resources.

The various resources listed below are aligned to the same standard, (7EE04) taken from the CCSM ( Common Core Standards For Mathematics) as the Expressions and equations Worksheet shown above.

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

  • Solve word problems leading to equations of the form  px  +  q  =  r  and  p ( x  +  q ) =  r , where  p ,  q , and  r  are specific rational numbers . Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.  For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
  • Solve word problems leading to inequalities of the form  px  +  q  >  r  or  px  +  q  <  r , where  p ,  q , and  r  are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.  For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Example/Guidance

  • Solving Simple Equations in 2 Steps

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Solve real-life and mathematical problems using numerical and algebraic expressions and equations

  • Equations with subtraction  e.g. x – 4 = 2 (From Worksheet)
  • Equations with division  e.g. n/2 = 12 (From Worksheet)
  • Subtraction & addition equations (1 of 2)  e.g. a + 3 = 7 and x – 9 = 11 (From Worksheet)
  • Subtraction & addition equations (2 of 2)  e.g. a + 3 = 7 and x – 9 = 11 (From Worksheet)
  • Multiplication & division equations (1 of 2)  e.g. 3n = 12 and a/7 = 3 (From Worksheet)
  • Multiplication & division equations (2 of 2)  e.g. 3n = 12 and a/7 = 3 (From Worksheet)
  • Addition, subtraction, multiplication & division equations  (From Worksheet)
  • Solving equations in two steps (1 of 4)  e.g. 5n + 4 = 29 (From Worksheet)
  • Solving equations in two steps (2 of 4)  e.g. a/4 + 3 = 7 (From Worksheet)
  • Solving equations in two steps (3 of 4)  e.g. 7n – 3 = 18 (From Worksheet)
  • Solving equations in two steps (4 of 4)  e.g. b/9 – 4 = 6 (From Worksheet)

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  1. Inequalities Word Problems Worksheet With Answers / Solving Linear

    solving equations and inequalities word problems worksheet

  2. Inequalities Worksheets with Answer Key

    solving equations and inequalities word problems worksheet

  3. Inequalities Worksheet With Answers

    solving equations and inequalities word problems worksheet

  4. Absolute Value Inequalities Worksheet With Answers

    solving equations and inequalities word problems worksheet

  5. Rational Inequalities Worksheet Doc

    solving equations and inequalities word problems worksheet

  6. Solving Equations and Inequalities Worksheets with Answer Key

    solving equations and inequalities word problems worksheet

VIDEO

  1. Solving Word Problems Involving Quadratic Inequalities

  2. Word Problems Involving Inequalities

  3. Writing Inequalities from Word Problems with 2 variables

  4. Solving Inequalities Word Problem EX2

  5. Inequalities Word Problems Worksheet pt1

  6. worksheet grade 6 main points solving equations inequalities properties of equality Moath Aljebawi

COMMENTS

  1. Equation Word Problems Worksheets

    This compilation of a meticulously drafted equation word problems worksheets is designed to get students to write and solve a variety of one-step, two-step and multi-step equations that involve integers, fractions, and decimals. These worksheets are best suited for students in grade 6 through high school.

  2. Equations and Word Problems

    These free equations and word problems worksheets will help your students practice writing and solving equations that match real-world story problems. Your students will write equations to match problems like "Kelly is 8 years younger than her sister. The sum of their ages is 44 years.

  3. Inequalities Word Problems Worksheets

    Inequalities word problems worksheets helps kids to improve their speed, accuracy, logical and reasoning skills in performing simple calculations related to the topic of inequalities. Inequalities word problems worksheets are also helpful for students to prepare for various competitive exams.

  4. Inequalities Worksheets

    View Answers Solving Inequalities Worksheet 4 - Here is a twelve problem worksheet featuring one-step inequalities. Use inverse operations or mental math to solve for x. Solving Inequalities Worksheet 4 RTF Solving Inequalities Worksheet 4 PDF Preview Solving Inequalities Worksheet 4 in Your Browser View Answers

  5. Word problems systems of equations and inequalities

    Below you can download some free math worksheets and practice. Systems-of-Equations-and-Inequalities-Word-problems-easy.pdf. Download. Downloads: 36256 x. This free worksheet contains 10 assignments each with 24 questions with answers. Example of one question: Watch below how to solve this example:

  6. Equations and Inequalities Word Problems Worksheets

    These worksheets and lessons teach students how to write equations and inequalities that are based on word problems. This will empower your students to solve much more complex problem types that will require critical thinking skills that they should be ready for at the high school level.

  7. Writing Inequalities from Word Problems

    Step 1) Read the word problem carefully and change the word problem into algebra. use the language of inequalities table to help you select the right inequality Step 2) Use algebra to solve the word problem Step 3) Rewrite the inequality using algebra.

  8. Algebra 2 Worksheets

    These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade. Click here for a Detailed Description of all the Equations Worksheets. Quick Link for All Equations Worksheets Click the image to be taken to that Equations Worksheet. Multiple Step Integer Equations Equations Worksheets

  9. Inequalities word problems (practice)

    6th grade > Equations & inequalities > Intro to inequalities with variables Inequalities word problems Google Classroom Kwame must earn more than 16 stars per day to get a prize from the classroom treasure box. Write an inequality that describes S , the number of stars Kwame must earn per day to get a prize from the classroom treasure box. Stuck?

  10. Equations and Inequalities Worksheets

    Include Equations Worksheet Answer Page. Now you are ready to create your Equations Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. Click here for More Algebra 2 - Equations and Inequalities Worksheets.

  11. Solving Inequality Word Questions

    Solving Inequality Word Questions (You might like to read Introduction to Inequalities and Solving Inequalities first.) In Algebra we have "inequality" questions like: Sam and Alex play in the same soccer team. Last Saturday Alex scored 3 more goals than Sam, but together they scored less than 9 goals.

  12. Equations & inequalities

    Solving equations is a superpower. It means we can model a situation with an equation in any way that makes sense to us, even with an unknown value in the middle. ... Inequalities word problems Get 3 of 4 questions to level up! Quiz 3. Level up on the above skills and collect up to 400 Mastery points Start quiz.

  13. Equations & inequalities word problems (practice)

    Algebra 2 > Modeling > Modeling with two variables Equations & inequalities word problems Google Classroom The Smiths and the Johnsons were competing in the final leg of the Amazing Race. In their race to the finish, the Smiths immediately took off on a 165 kilometer path traveling at an average speed of v kilometers per hour.

  14. Free Linear Inequalities Word Problems Worksheet

    The worksheet attached below will provide you with some practice using number lines to communicate your answers to inequality word problems. Solving a Linear Inequality Word Problem Example Age problems are common applications that you will see when solving linear inequality word problems.

  15. Inequalities Word Problem Worksheet

    Answers to Inequalities Word Problem Worksheet 1) No more than 12 weeks 4) At least 12 more sessions 6) More than 12.5 weeks. 8) No solution. 10 12 14 16 10) x £ -1 : 18 2) No more than 12.7 miles

  16. Inequalities Worksheets with Answer Key

    Solving Equations and Inequalities Worksheets One Step Inequalities Worksheets Two Step Inequalities Worksheets Linear Inequalities Worksheets Multi Step Inequalities Worksheets Quadratic Inequalities Worksheets Absolute Value Inequalities Worksheets Writing Inequalities Worksheets Rational Inequalities Worksheets

  17. Solving equations & inequalities

    Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions. Linear equations with variables on both sides Learn Why we do the same thing to both sides: Variable on both sides Intro to equations with variables on both sides

  18. Equations and Inequalities Worksheets

    Equations and Inequalities Worksheets. Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. An equation is a statement that asserts the equality of two expressions and a linear inequality is an inequality which involves a linear function. It shows the data which is not equal in graph form.

  19. Inequalities Word Problems Worksheet

    Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p ( x + q) = r, where p , q, and r are specific rational numbers.

  20. Systems of Equations and Inequalities Worksheets

    This systems of equations worksheet is a good resource for students in the 5th Grade, 6th Grade, 7th Grade, and 8th Grade. This systems of equations worksheet will produce problems for solving two variable systems of inequalities graphically. You may select four different types of problems. This systems of equations worksheet will produce eight ...

  21. Systems of inequalities word problems (practice)

    Choose 1 answer: The bathroom has enough water and shampoo. A The bathroom has enough water and shampoo. The bathroom has enough water but not enough shampoo. B The bathroom has enough water but not enough shampoo. The bathroom has enough shampoo but not enough water. C The bathroom has enough shampoo but not enough water.

  22. Free Printable Math Worksheets for Algebra 1

    Finding angles of triangles. Finding side lengths of triangles. Statistics. Visualizing data. Center and spread of data. Scatter plots. Using statistical models. Free Algebra 1 worksheets created with Infinite Algebra 1. Printable in convenient PDF format.

  23. Inequalities Practice Questions

    Click here for Answers. inequality. Practice Questions. Previous: Graphical Inequalities Practice Questions. Next: Cumulative Frequency and Box Plot Practice Questions. The Corbettmaths Practice Questions on inequalities.