Practice Solving Linear Equations in Math

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

Quick Recap

The process of finding the value of the variable that makes a linear equation true, using inverse operations to isolate the variable on one side of the equals sign. A linear equation has the variable raised only to the first power, producing exactly one solution.

Undo what's done to xx by doing the opposite: if x+5x + 5, subtract 5.

Showing a random 20 of 50 problems.

Example 1

medium
Sarah is 33 years older than her brother Tom. The sum of their ages is 2525. How old is each?

Example 2

challenge
Solve 2xโˆ’35โˆ’x+12=1\frac{2x - 3}{5} - \frac{x + 1}{2} = 1.

Example 3

hard
Solve 2x+13=xโˆ’22\frac{2x + 1}{3} = \frac{x - 2}{2}.

Example 4

challenge
For what value of kk does the equation 3x+7=kxโˆ’23x + 7 = kx - 2 have NO solution?

Example 5

medium
Solve 0.4x+1.2=3.60.4x + 1.2 = 3.6.

Example 6

easy
Solve x5โˆ’2=3\frac{x}{5} - 2 = 3.

Example 7

easy
Solve 5xโˆ’3=125x - 3 = 12.

Example 8

medium
Solve 2(3xโˆ’4)=5x+62(3x - 4) = 5x + 6.

Example 9

medium
Solve 4x+7=2x+234x + 7 = 2x + 23.

Example 10

medium
Solve 3(x+4)=213(x + 4) = 21.

Example 11

hard
A father is three times as old as his son. In 1212 years, he will be twice as old as his son. Find the son's current age.

Example 12

medium
Solve 2xโˆ’13=x+24\frac{2x - 1}{3} = \frac{x + 2}{4}.

Example 13

medium
Solve 12x+13x=10\frac{1}{2}x + \frac{1}{3}x = 10.

Example 14

easy
Solve x3+2=7\frac{x}{3} + 2 = 7.

Example 15

easy
Solve x+5=12x + 5 = 12.

Example 16

medium
Solve xโˆ’45=3\frac{x - 4}{5} = 3.

Example 17

easy
Solve x4=6\frac{x}{4} = 6.

Example 18

medium
Solve 5(xโˆ’3)=2x+95(x - 3) = 2x + 9.

Example 19

medium
Solve 23x+5=11\frac{2}{3}x + 5 = 11.

Example 20

easy
Solve โˆ’x=7-x = 7.