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Pre-Algebra

Solving One-Step Equations

Lesson

A one-step equation can be solved by doing a single operation on both sides. The goal is to get the variable (xx) all by itself.

Whatever operation is being done to the variable, you do the inverse operation to both sides:

  • Addition ↔ Subtraction
  • Multiplication ↔ Division

Worked example 1

x+3=10x + 3 = 10

We see + 3+\,3, so we subtract 3 from both sides:

x+3−3=10−3x + 3 - 3 = 10 - 3
x=7x = 7

Worked example 2

5x=205x = 20

We see multiplication by 5, so we divide both sides by 5:

5x5=205\frac{5x}{5} = \frac{20}{5}
x=4x = 4

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

x+1=5x + 1 = 5

Problem 2

x−2=6x - 2 = 6

Problem 3

2x=102x = 10

Problem 4

x3=2\frac{x}{3} = 2

Practice

Standard problems matching the lesson.

Problem 5

x+7=12x + 7 = 12

Problem 6

x−4=9x - 4 = 9

Problem 7

3x=213x = 21

Problem 8

x4=6\frac{x}{4} = 6

Problem 9

x+15=8x + 15 = 8

Problem 10

x+9=15x + 9 = 15

Problem 11

x−6=2x - 6 = 2

Problem 12

6x=306x = 30

Problem 13

x5=4\frac{x}{5} = 4

Problem 14

x−12=−3x - 12 = -3

Problem 15

−3x=12-3x = 12

Problem 16

14+x=2314 + x = 23

Problem 17

11=x+411 = x + 4

Problem 18

5x=−255x = -25

Problem 19

x−2=6\frac{x}{-2} = 6

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 20

x+24=11x + 24 = 11

Problem 21

x−7=−19x - 7 = -19

Problem 22

−7x=49-7x = 49

Problem 23

x−3=8\frac{x}{-3} = 8

Problem 24

100=4x100 = 4x

Problem 25

−16=x−9-16 = x - 9