Practice Multi-Step Equations in Math

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

Quick Recap

Solving equations that require more than one inverse operationβ€”typically involving distributing, combining like terms, and moving variables to one side before isolating the variable.

A one-step equation is like unwrapping one layer of packaging. A multi-step equation has several layers: first simplify each side (distribute, combine like terms), then peel off operations one at a time until xx stands alone. Think of it as cleaning up a messy room before finding what you're looking for.

Showing a random 20 of 50 problems.

Example 1

easy
Solve βˆ’2x+7=1-2x + 7 = 1.

Example 2

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

Example 3

easy
Solve 6x+4=4x+106x + 4 = 4x + 10.

Example 4

medium
Solve 4(x+1)βˆ’2=3(xβˆ’2)+54(x + 1) - 2 = 3(x - 2) + 5.

Example 5

hard
Solve for xx in terms of aa and bb: a(xβˆ’b)=bx+aa(x - b) = bx + a.

Example 6

medium
Solve 4(xβˆ’3)+2x=184(x - 3) + 2x = 18.

Example 7

easy
Solve 3(x+2)=153(x + 2) = 15.

Example 8

hard
Solve x+34βˆ’xβˆ’13=16\frac{x + 3}{4} - \frac{x - 1}{3} = \frac{1}{6}.

Example 9

hard
Solve 2xβˆ’15=x+43\frac{2x - 1}{5} = \frac{x + 4}{3}.

Example 10

easy
Solve 3(x+2)βˆ’4=143(x + 2) - 4 = 14.

Example 11

medium
Identify whether 3(x+2)=3x+63(x + 2) = 3x + 6 has one, no, or infinitely many solutions.

Example 12

challenge
A father is three times his son's age. In 1010 years, the father will be twice the son's age. Find their current ages.

Example 13

medium
Solve 7βˆ’2(xβˆ’4)=37 - 2(x - 4) = 3.

Example 14

medium
Solve 2(3xβˆ’1)+4=5x+72(3x - 1) + 4 = 5x + 7.

Example 15

medium
Solve 4(xβˆ’2)=4x+14(x - 2) = 4x + 1.

Example 16

hard
A rectangle has perimeter 4444 cm. Its length is 44 more than twice its width. Find the dimensions.

Example 17

medium
Solve 3x+5=2(x+7)3x + 5 = 2(x + 7).

Example 18

easy
Solve 2(x+3)=142(x + 3) = 14.

Example 19

medium
Solve x+12βˆ’xβˆ’34=3\frac{x+1}{2} - \frac{x-3}{4} = 3.

Example 20

challenge
A number doubled, plus 77, equals three times the number minus 22. Find the number.