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• solve\:for\:x,\:2x-4=10
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• What is Solve for x in math?
• Solve for x in math means finding the value of x that would make the equation true.
• How do you get X by itself?
• To get a variable by itself a combination of algebraic techniques is requiered. The distributive property, the addition and subtraction properties of equality to move all the terms containing x to one side of the equation, the multiplication and division properties of equality to eliminate any coefficients.
• How do you solve the equation for different variables step-by-step?
• To solve the equation for different variables step-by-step clear any fractions by multiplying both sides of the equation by the LCM of the denominators. Get all the terms with the wanted variable on one side of the equation and all the other terms on the other side. Isolate the variable, and solve for the variable by undoing any arithmetic operations that were used to isolate it.

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How to Solve for X

Last Updated: March 20, 2024 Fact Checked

This article was co-authored by David Jia . David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 798,806 times.

There are a number of ways to solve for x, whether you're working with exponents and radicals or if you just have to do some division or multiplication. No matter what process you use, you always have to find a way to isolate x on one side of the equation so you can find its value. Here's how to do it:

Using a Basic Linear Equation

• 2 2 (x+3) + 9 - 5 = 32

• 4(x+3) + 9 - 5 = 32

• 4x + 12 + 9 - 5 = 32

• 4x+21-5 = 32
• 4x + 16 - 16 = 32 - 16

• 4x/4 = 16/4

• 2 2 (x+3)+ 9 - 5 = 32
• 2 2 (4+3)+ 9 - 5 = 32
• 2 2 (7) + 9 - 5 = 32
• 4(7) + 9 - 5 = 32
• 28 + 9 - 5 = 32
• 37 - 5 = 32

With Exponents

• 2x 2 + 12 = 44

• 2x 2 +12-12 = 44-12

• (2x 2 )/2 = 32/2
• 4 Take the square root of each side of the equation. [6] X Research source Taking the square root of x 2 will cancel it out. So, take the square root of both sides. You'll get x left over on one side and plus or minus the square root of 16, 4, on the other side. Therefore, x = ±4.
• 2(4) 2 + 12 = 44
• 2(16) + 12 = 44
• 32 + 12 = 44

Using Fractions

• (x + 3)/6 = 2/3

• (x + 3) x 3 = 3x + 9
• 3x + 9 = 12

• 3x + 9 - 9 = 12 - 9

• (1 + 3)/6 = 2/3

Using Radical Signs

• √(2x+9) - 5 = 0

• √(2x+9) - 5 + 5 = 0 + 5
• √(2x+9) = 5

• (√(2x+9)) 2 = 5 2
• 2x + 9 = 25

• 2x + 9 - 9 = 25 - 9

• √(2(8)+9) - 5 = 0
• √(16+9) - 5 = 0
• √(25) - 5 = 0

Using Absolute Value

• |4x +2| - 6 = 8

• |4x +2| - 6 + 6 = 8 + 6
• |4x +2| = 14

• 4x + 2 = 14
• 4x + 2 - 2 = 14 -2

• 4x + 2 = -14
• 4x + 2 - 2 = -14 - 2
• 4x/4 = -16/4

• |4(3) +2| - 6 = 8
• |12 +2| - 6 = 8
• |14| - 6 = 8
• |4(-4) +2| - 6 = 8
• |-16 +2| - 6 = 8
• |-14| - 6 = 8

Practice Problems and Answers

Expert Q&A

• To check your work, plug the value of x back into the original equation and solve. Thanks Helpful 0 Not Helpful 0
• Radicals, or roots, are another way of representing exponents. The square root of x = x^1/2. Thanks Helpful 0 Not Helpful 0

You Might Also Like

• ↑ David Jia. Academic Tutor. Expert Interview. 23 February 2021
• ↑ https://tutorial.math.lamar.edu/Classes/Alg/SolveLinearEqns.aspx
• ↑ https://www.purplemath.com/modules/solvelin.htm
• ↑ https://sciencing.com/tips-for-solving-algebraic-equations-13712207.html
• ↑ https://www.youtube.com/watch?v=LMS1NR4gZN8
• ↑ https://www.mathsisfun.com/algebra/fractions-algebra.html
• ↑ http://www.mathsisfun.com/algebra/radical-equations-solving.html
• ↑ http://www.sosmath.com/algebra/solve/solve0/solve0.html

About This Article

To solve for x in a basic linear equation, start by resolving the exponent using the order of operations. Then, isolate the variable to get your answer. To solve for x when the equation includes an exponent, start by isolating the term with the exponent. Then, isolate the variable with the exponent by dividing both sides by the coefficient of the x term to get your answer. If the equation has fractions, start by cross-multiplying the fractions. Then, combine like terms and isolate x by dividing each term by the x coefficient. If you want to learn how to solve for x if the equation has radicals or absolute values, keep reading the article! Did this summary help you? Yes No

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Solve for x

Solve for x is all related to finding the value of x in an equation of one variable that is x or with different variables like finding x in terms of y. When we find the value of x and substitute it in the equation, we should get L.H.S = R.H.S.

What Does Solve for x Mean?

Solve for x means finding the value of x for which the equation holds true. i.e when we find the value of x and substitute in the equation, we should get L.H.S = R.H.S If I ask you to solve the equation 'x + 1 = 2' that would mean finding some value for x that satisfies the equation. Do you think x = 1 is the solution to this equation? Substitute it in the equation and see. 1 + 1 = 2 2 = 2 L.H.S = R.H.S That’s what solving for x is all about.

How Do You Solve for x?

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result. Let’s start with a simple equation as, x + 2 = 7 How do you get x by itself? Subtract 2 from both sides ⇒ x + 2 - 2 = 7 - 2 ⇒ x = 5 Now, check the answer, x = 5 by substituting it back into the equation. We get 5 + 2= 7. L.H.S = R.H.S

Solve for x in the Triangle

Solve for x" the unknown side or angle in a triangle we can use properties of triangle or the Pythagorean theorem.

Let us understand solve for x in a triangle with the help of an example.

△ ABC is right-angled at B with two of its legs measuring 7 units and 24 units. Find the hypotenuse x.

In △ABC by using the Pythagorean theorem,

we get AC 2 = AB 2 + BC 2

⇒ x 2 = 7 2 + 24 2

⇒ x 2 = 49 + 576

⇒ x 2 = 625

⇒ x = 25 units

Solve for x to find Missing Angle of Triangle

Suppose angle A = 50°, angle B = 60°, and angle C = x are the angles of a triangle. ABC. By using the angle sum property we can find the value of x.

angle A + angle B + angle C = 180 degrees.

50° + 60° + x° = 180° ⇒ x = 70°

Solve for x in Fractions

Solve for x in fractions , we simply do the cross multiplication and simplify the equation to find x.

For example: Solve for x for equation ⇒ 2/5 = x/10.

Cross multiply the fractions ⇒ 2 × 10 = 5 × x Solve the equation for x ⇒ x = 20 / 5 Simplify for x ⇒ x = 4 To verify the x value put the result, 4 back into the given equation ⇒ 2/5 = 4/10 Cross multiply the fractions ⇒ 2 × 10 = 4 × 5 ⇒ 20 = 20 L.H.S = R.H.S

Solve for x Equations

We can use a system of equations solver to find the value of x when we have equations with different variables.

We solve one of the equations for the x variable (solve for x in terms of y) and then substitute it in the second equation, and then solve for the y variable.

Finally, we substitute the value of the x variable that we found in one of the equations and solve for the other variable.

Let us understand solve for x and y with the help of an example.

For example, Solve for x: 2x - y = 5, 3x + 2y = 11

⇒ 2x - y = 5

Adding y on both sides we get,

⇒ 2x - y + y = 5 + y

⇒ 2x = 5 + y

⇒ x = (5 + y) / 2

Above equation is known as x in terms of y.

Substitute x = (5 + y) / 2 in second equation 3(5 + y) / 2 + 2y = 11

⇒ (15 + 3y) / 2 + 2y = 11

⇒ (15 + 3y + 4y) / 2 = 11

⇒ (15 + 7y) / 2 = 11

⇒15 +7y = 22

⇒ 7y = 22 - 15

Now, substitute y = 1 in x = (5+y) / 2

⇒ x = (5 + 1) / 2

⇒ 6 / 2 = 3

Thus, the solution of the given system of equations is x = 3 and y = 1.

Important Notes on Solve for x

• To solve for x (the unknown variable in the equation), apply arithmetic operations to isolate the variable.
• For solving 'x' number of equations we need exactly 'x' number of variables.
• Solve for x and y can be done by the substitution method, elimination method, cross-multiplication method, etc.

☛ Related Articles

Here is a solve for x calculator for you to get your answers quickly. Try now. Also, check out these interesting articles to know more about solve for x.

• System of Equations Solver
• Polynomial Equations
• Linear Equations
• Linear Equations in Two Variables

Solve for x Examples

Example1: Solve for x: 2 ( 3x + 1 ) + 3 ( 5x + 2 ) = x - 1

Solution: 2 (3x + 1) + 3 (5x + 2) = x - 1

⇒ 6x + 2 + 15x + 6 = x - 1

⇒ 8 + 21x = x - 1

⇒ x = -9/20

Example 2: It is given that x is the one side of the chessboard and it is smaller than its perimeter by 18 inches. Form an equation and solve for x?

Solution: The side of chessboard = 'x' inches

Since the chessboard is square (all sides are equal), therefore its perimeter will be '4x' inches

According to the given condition,

Perimeter = x + 18

⇒ 4x = x + 18

⇒ 4x - x = 18

The side of the chessboard is 6 inches.

Example 3: The ages of Roony and Herald are 5x and 7x. If four years later, the sum of their ages will be 56 years, then form an equation and solve for x.

Solution: The Rooney and Herald's age is 5x and 7x.

The sum of their ages after 4 years = 56

According to given condition,

⇒ (5x+4) + (7x+4) = 56

⇒ 5x + 7x + 4 + 4 = 56

⇒ 12x + 8 = 56

⇒ 12x = 56 - 8

⇒ x = 48/12

⇒ x = 4 The age of Roony = 5 × 4 = 20 years The age of Herald = 7× 4 = 28 years

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Practice Questions

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FAQs on Solve For x

How do you solve for x in a bracket.

To solve for x in a bracket we use distributive law and remove the bracket, move all the x terms to one side and constant to the other side and find the unknown x. For example, 2(x−3) = 4 By using distributive law, 2x - 6 = 4 ⇒ 2x = 4 + 6 ⇒ 2x = 10 ⇒ x = 10/2 ⇒ x = 5

How Do You Solve for x in a Fraction?

To solve for x in fractions we have to eliminate the denominator by cross multiplication and then solve for x. For example, x/4 + 1/2 = 5/2 ⇒ (2x+4)/8 = 5/2 By doing cross multiplication we get, 2(2x + 4) = 8(5) ⇒ 4x + 8 = 40 ⇒ 4x = 40 - 8 ⇒ 4x = 32 ⇒ x = 32 / 4 ⇒ x = 8

How Do You Solve for x for the Equation 4x + 2 = -8?

To solve for x follow the points.

• Start with 4x + 2 = -8
• Subtract 2 from both sides: 4x = -8 - 2 = -10
• Divide by 4: x = -10 ÷ 4 = -5/2

How Do You Solve for x for the Equation 3x - 7 = 26?

• Start with 3x - 7 = 26
• Add 7 to both sides: 3x - 7 + 7 = 26 + 7
• Calculate: 3x = 33
• Divide by 3: x = 33 ÷ 3

How Do You Solve for x in Vertical Angles?

Vertical angles are congruent , or we can say they have same measure. For example, if a vertical angle equals 2x and the other equals 90 - x, we would simply form an equation 2x = 90 - x. 2x = 90 - x Add x to both sides, 2x + x = 90 -x + x 3x = 90 x = 30

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QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

• The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
• The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
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Solving Equations

What is an equation.

An equation says that two things are equal. It will have an equals sign "=" like this:

That equations says:

what is on the left (x − 2)  equals  what is on the right (4)

So an equation is like a statement " this equals that "

What is a Solution?

A Solution is a value we can put in place of a variable (such as x ) that makes the equation true .

Example: x − 2 = 4

When we put 6 in place of x we get:

which is true

So x = 6 is a solution.

How about other values for x ?

• For x=5 we get "5−2=4" which is not true , so x=5 is not a solution .
• For x=9 we get "9−2=4" which is not true , so x=9 is not a solution .

In this case x = 6 is the only solution.

You might like to practice solving some animated equations .

More Than One Solution

There can be more than one solution.

Example: (x−3)(x−2) = 0

When x is 3 we get:

(3−3)(3−2) = 0 × 1 = 0

And when x is 2 we get:

(2−3)(2−2) = (−1) × 0 = 0

which is also true

So the solutions are:

x = 3 , or x = 2

When we gather all solutions together it is called a Solution Set

The above solution set is: {2, 3}

Solutions Everywhere!

Some equations are true for all allowed values and are then called Identities

Example: sin(−θ) = −sin(θ) is one of the Trigonometric Identities

Let's try θ = 30°:

sin(−30°) = −0.5 and

−sin(30°) = −0.5

So it is true for θ = 30°

Let's try θ = 90°:

sin(−90°) = −1 and

−sin(90°) = −1

So it is also true for θ = 90°

Is it true for all values of θ ? Try some values for yourself!

How to Solve an Equation

There is no "one perfect way" to solve all equations.

A Useful Goal

But we often get success when our goal is to end up with:

x = something

In other words, we want to move everything except "x" (or whatever name the variable has) over to the right hand side.

Example: Solve 3x−6 = 9

Now we have x = something ,

and a short calculation reveals that x = 5

Like a Puzzle

In fact, solving an equation is just like solving a puzzle. And like puzzles, there are things we can (and cannot) do.

Here are some things we can do:

• Add or Subtract the same value from both sides
• Clear out any fractions by Multiplying every term by the bottom parts
• Divide every term by the same nonzero value
• Combine Like Terms
• Expanding (the opposite of factoring) may also help
• Recognizing a pattern, such as the difference of squares
• Sometimes we can apply a function to both sides (e.g. square both sides)

Example: Solve √(x/2) = 3

And the more "tricks" and techniques you learn the better you will get.

Special Equations

There are special ways of solving some types of equations. Learn how to ...

• solve Quadratic Equations
• solve Radical Equations
• solve Equations with Sine, Cosine and Tangent

Check Your Solutions

You should always check that your "solution" really is a solution.

How To Check

Take the solution(s) and put them in the original equation to see if they really work.

Example: solve for x:

2x x − 3 + 3 = 6 x − 3     (x≠3)

We have said x≠3 to avoid a division by zero.

Let's multiply through by (x − 3) :

2x + 3(x−3) = 6

Bring the 6 to the left:

2x + 3(x−3) − 6 = 0

Expand and solve:

2x + 3x − 9 − 6 = 0

5x − 15 = 0

5(x − 3) = 0

Which can be solved by having x=3

Let us check x=3 using the original question:

2 × 3 3 − 3 + 3  =   6 3 − 3

Hang On: 3 − 3 = 0 That means dividing by Zero!

And anyway, we said at the top that x≠3 , so ...

x = 3 does not actually work, and so:

There is No Solution!

That was interesting ... we thought we had found a solution, but when we looked back at the question we found it wasn't allowed!

This gives us a moral lesson:

"Solving" only gives us possible solutions, they need to be checked!

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