Practice Isolating Variable in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Rearranging an equation by applying inverse operations until the variable stands alone on one side.

Peel away everything around $x$ until only $x$ remains: $x =$ answer.

Showing a random 20 of 59 problems.

Example 1

challenge

Solve for

x

ax+b=c

(with

a\ne0

), in terms of

a,b,c

Example 2

medium

Isolate

x

2(x+3)=14

Example 3

medium

Solve for

h

V = \pi r^2 h

Example 4

easy

Isolate

x

x+8=15

Example 5

hard

Solve for

r

A = P(1 + rt)

(simple interest).

Example 6

challenge

Solve for

x

\log_2(x - 1) + \log_2(x + 1) = 3

Example 7

easy

Solve for

x

\frac{2x}{3} = 8

Example 8

hard

Solve for

x

2(3x - 1) - 4(x + 5) = 6

Example 9

medium

Solve for

b

A=\frac{a+b}{2}

Example 10

medium

Solve for

r

C=2\pi r

Example 11

easy

Isolate

x

2x=7

Example 12

easy

Solve for

x

-3x = 21

Example 13

easy

Isolate

x

x+\frac{1}{2}=2

Example 14

medium

Isolate

x

5x-3=2x+9

Example 15

hard

Solve for

x

in terms of

a, b

\frac{x - a}{b} = \frac{x + b}{a}

(

a, b \neq 0

a \neq b

Example 16

easy

Fill in the blank so that the solution is

x = 6

\frac{x}{2} + \_\_ = 10

Example 17

medium

Solve for

x

\frac{x - 3}{4} = \frac{x + 1}{6}

Example 18

medium

Solve for

x

3(x - 4) = 18

Example 19

hard

Solve for

x

\sqrt{2x + 5} = 7

Example 20

easy

Solve for

x

x + 12 = 5

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Related Concepts

Inverse Operations Equations Solving Linear Equations