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 59 problems.

Example 1

medium
Solve 5โˆ’2x=135 - 2x = 13.

Example 2

challenge
Train A leaves a station at 6060 mph. Two hours later, train B leaves the same station traveling the same direction at 8080 mph. How many hours after B's departure does B catch A?

Example 3

easy
Solve 5xโˆ’3=125x - 3 = 12.

Example 4

easy
Solve โˆ’3x=18-3x = 18.

Example 5

medium
Solve 6โˆ’2(x+1)=4xโˆ’86 - 2(x + 1) = 4x - 8.

Example 6

easy
Solve 5xโˆ’3=175x - 3 = 17.

Example 7

medium
Solve x+34=5\frac{x + 3}{4} = 5.

Example 8

easy
Solve xโˆ’8=3x - 8 = 3.

Example 9

medium
Sam solves x+6=20x + 6 = 20 like this: "x=20+6x = 20 + 6, so x=26x = 26." Find Sam's mistake and enter the correct value of xx.

Example 10

medium
Solve 3(x+2)โˆ’4(xโˆ’1)=53(x + 2) - 4(x - 1) = 5.

Example 11

challenge
Solve for xx in terms of aa and bb: a(xโˆ’b)=b(x+a)a(x - b) = b(x + a), where aโ‰ ba \neq b.

Example 12

easy
Solve 7x=567x = 56.

Example 13

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

Example 14

medium
Solve 6โˆ’x=96 - x = 9. (Compare with its twin: xโˆ’6=9x - 6 = 9.)

Example 15

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

Example 16

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

Example 17

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

Example 18

easy
Solve 4x+9=334x + 9 = 33.

Example 19

challenge
Anna can paint a room in 44 hours. Ben can paint it in 66 hours. How long if they work together?

Example 20

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