solving two step inequalities word problems worksheet

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Two-Step Inequalities Worksheets

Ratchet up skills with our printable two step inequalities worksheets curated for students in grade 7, grade 8, and high school. It takes two steps to solve these inequalities that contain more than one operation. Undo addition or subtraction first followed by division or multiplication using inverse operations to isolate the variable. Transcend through easy, moderate and difficult levels and master solving and graphing two-step inequalities involving whole numbers, integers, decimals, and fractions like a pro. Tread just two steps, download and print and access our free two step inequalities worksheets!

Identifying Solutions to Two-Step Inequalities

Don't let the four options flummox your 7th grade students. Get them to follow a trial-and-error method by substituting each option in the inequality and solve it. Identify and circle the solutions that satisfy each inequality.

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Solving Two-Step Inequalities

The mantra is to get the variable isolated on one side by performing inverse operations on either side. First eliminate the constants, followed by coefficients and solve the two-step inequalities with a never-before ease.

Solving and Graphing Two-Step Inequalities

Ally solving with plotting with our printable two step inequalities worksheets and work toward your pursuit of finding and graphing the relative value on number lines with an open or closed circle and arrow mark indicating the solution range.

Spotting the Solutions in Interval Notations

Grow the skills of your students in grade 7 and grade 8 in solving two-step inequalities in meteoric proportions, as they steer clear through these two step inequalities pdfs finding the range of solutions from the four intervals given.

Solving Two-Step Inequalities | Fractions and Decimals

By turns interesting and challenging these printable two step inequalities worksheets with twin number types: fractions and decimals, your students are sure to hit new heights in solving these inequalities.

Finding Solutions and Graphing Two-Step Inequalities

With a hard to beat versatility, these solving and graphing two-step inequalities get students in 7th grade and 8th grade to solve the inequalities with fraction and decimal coefficients and constants in two-steps and graph them on a number line.

Identifying Solution Graphs

Identifying the correct solution graph for each two-step inequality is not beyond your ken. High school students solve the inequality by using the additive and multiplicative inverses to isolate the variable and identify the graph that best describes the solution.

Identifying Two-Step Inequality from the Number Line

Observe the number line keenly, identify the relative value, comprehend if the inequality is inclusive or strict from the open or closed circle, look at the direction of the ray to figure out the solution. Choose the two-step inequality whose solution this could possibly be.

Translating Inequality Phrases Worksheets

In this part of our two-step inequalities pdf worksheets, grade 7 and grade 8 students get adequate practice in setting up a two-step inequality by translating verbal descriptions of real-life scenarios. Watch out! You may have to use variables on both sides.

(12 Worksheets)

Related Worksheets

» One Step Inequalities

» Multi Step Inequalities

» Compound Inequalities

» Absolute Value Inequalities

» Two Step Equations

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Inequalities Word Problems Worksheets

Inequalities word problems worksheets can help encourage students to read and think about the questions, rather than simply recognizing a pattern to the solutions.Inequalities word problems worksheet come with the answer key and detailed solutions which the students can refer to anytime.

Benefits of Inequalities Word Problems Worksheets

Inequalities word problems worksheets help kids to improve their speed, accuracy, logical and reasoning skills.

Inequalities word problems worksheets gives students the opportunity to solve a wide variety of problems helping them to build a robust mathematical foundation. 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.

These worksheets come with visual simulation for students to see the problems in action, and provides a detailed step-by-step solution for students to understand the process better, and a worksheet properly explained about the Inequalities.

Download Inequalities Word Problems Worksheet PDFs

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

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• 7th Grade Inequalities Worksheets

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Course: 7th grade   >   Unit 6

Two-step inequalities.

• Two-step inequality word problem: apples
• Two-step inequality word problem: R&B
• Two-step inequality word problems
• (Choice A)   A
• (Choice B)   B
• (Choice C)   C
• (Choice D)   D

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Two-Step Inequalities Worksheets

The free printables in this section require students to solve two-step inequations and plot them graphically on number lines.

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Two-Step Inequality (Word Problems) Worksheet

The non-equal comparison made between two numbers or mathematical expressions is known as inequality. Inequality shows that an expression is either smaller than or greater than another expression. Those inequalities that involve two steps in solving are known as two-step inequalities. In a layman’s language, this means that you will have to multiply, divide, add, or subtract two times in order to solve the inequality that you are presented with. Word problems related to two-step inequality are very helpful to understand inequalities as they are usually associated with the problems of real life. 

Teaching to Solve Two-step Inequality (Word Problems) Easily

Four easy steps that are discussed below can be used to solve two-step inequality word problems easily.

Step 1: Interpret the word problem properly and form an inequality out of it. 

Step 2: Get the variable on one side of the inequality by either adding or subtracting the constant.

Step 3: Either divide or multiply so that the coefficient on the term can be cancelled out. 

Step 4: One important thing that you will always have to keep in mind is that while you are performing the operation of division or multiplication, the inequality sign changes its symbol.

Why Should You Solve Two-step Inequality (Word Problems) Worksheet for Your Students?

• Solving two-step inequality word problems worksheets will help your students to understand in depth about the concept of inequalities.
• Solving word problems on inequality will enhance their performance of complex topics of inequalities.

Download Two-step Inequality (Word Problems) Worksheet Pdf

You can download and print these super fun two-step inequality (word problems) worksheet pdf for your students. You can also try our Two-Step Inequality (Word Problems) Problems and Two-Step Equation Word Problems Quiz as well for a better understanding of the concepts.

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Distributive Property (Factoring) Solve One-Step Equations Two-Step Inequality (Word Problems) Write And Solve Two-Step Equations (Level 2 Word Problems) Solve Two-Step Equations Write And Solve Two-Step Equations (Level 1 Word Problems)

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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.

Inequalities on a Number Line Worksheets

• Inequalities on a Number Line

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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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
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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:

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!

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:

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:

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

Free Printable Two-Step Inequalities worksheets

Math teachers, discover a valuable resource with our Free Printable Math Two-Step Inequalities worksheets! Enhance your students' learning experience and help them master essential skills in a fun and interactive way.

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Explore printable Two-Step Inequalities worksheets

Two-Step Inequalities worksheets are an essential resource for teachers looking to help their students master the fundamental concepts of Math, Algebra, and Inequalities. These worksheets provide a variety of exercises and problems that focus on Solving Inequalities, specifically those involving two-step processes. By incorporating these worksheets into their lesson plans, teachers can ensure that their students gain a strong understanding of the techniques and strategies required to tackle more complex algebraic problems. Additionally, the use of Two-Step Inequalities worksheets allows teachers to assess their students' progress and identify areas where further instruction or practice may be needed, ultimately leading to a more successful learning experience for all.

Quizizz, a popular online platform for creating and sharing educational content, offers a wide range of resources for teachers, including Two-Step Inequalities worksheets and other Math, Algebra, and Inequalities materials. By utilizing Quizizz in conjunction with traditional worksheets, teachers can create engaging, interactive lessons that cater to various learning styles and help students retain key concepts more effectively. Furthermore, Quizizz allows teachers to track student performance and progress, making it easier to identify areas where additional support or instruction may be necessary. With its extensive library of resources and user-friendly interface, Quizizz is an invaluable tool for teachers looking to enhance their students' understanding of Math, Algebra, and Inequalities, particularly when it comes to Solving Inequalities.

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Two Step Inequality Word Problem

Two Step Inequality Word Problem - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Two step inequalities date period, Study guide practice unit 5 test inequalities, Two step word problems, Solving inequalities date period, 1 read carefully and underline key words write a let, Concept 11 writing graphing inequalities, Inequality word problems, Solving two step inequalities.

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1. Two-Step Inequalities Date Period

2. study guide/ practice unit 5 test, inequalities, 3. two-step word problems, 4. solving inequalities date period, 5. 1 : read carefully and underline key words : write a let ..., 6. concept 11: writing & graphing inequalities, 7. inequality word problems, 8. 8.4 solving two-step inequalities.

• Two-step inequalities

Two-step inequalities are to one-step inequalities what two-step equations are to one-step equations – the same thing, but a bit more work is needed in order to solve them. Two-step inequalities are very easy to solve and the rules you have to adhere to are the same as for the one-step inequalities – remember that you need to change the sign of inequality when multiplying or dividing the whole inequality with a negative number. The order of operations will not come into play often since there are not many operations to perform here.

We will now show you on this example how this inequality looks like and what it takes to solve it:

4x + 8 > 20

The first thing you need to do is to put all the numbers on the right side and the variables on the left. Then perform the additions and subtractions . Like this:

4x > 20 – 8

The only thing left to do now is to divide the whole inequality by 4 to get the final, simplified result. Since the number we are dividing the inequality by is positive, it is not necessary to change the sign of inequality. Therefore:

4x > 12 |:4

And now we have the final result. If you wish to practice solving two-step inequalities a bit more, please feel free to use the worksheets below.

Two-step inequalities exams for teachers

Two-step inequalities worksheets for students.

Basic Mathematical Operations

• Addition and subtraction
• Multiplying
• Divisibility and factors
• Order of operations
• Greatest common factor
• Least common multiple
• Squares and square roots
• Naming decimal places
• Write numbers with words
• Verbal expressions in algebra
• Rounding numbers
• Convert percents, decimals and fractions
• Simplifying numerical fractions
• Proportions and similarity
• Calculating percents
• The Pythagorean theorem
• Quadrilaterals
• Solid figures
• One-step equations
• One-step equations – word problems
• Two-step equations
• Two-step equations – word problems
• Multi-step equations
• Multiplying polynomials
• Inequalities
• One-step inequalities
• Multi-step inequalities
• Coordinates
• Graphing linear equations
• The distance formula

Linear Equations

• Writing a linear equation
• Systems of linear equations
• Linear systems – word problems

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