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Pre-Algebra

Solving Two-Step Equations

Lesson

A two-step equation takes two operations to solve. The trick is to undo operations in reverse order: undo the addition or subtraction first, then the multiplication or division.

Why reverse order? Think about how the equation was built. To turn x=4x = 4 into 2x+3=112x + 3 = 11, you first multiply by 2, then add 3. To get back, you undo the steps in the opposite order: subtract 3 first, then divide by 2.

Worked example 1

2x+3=112x + 3 = 11

First, undo + 3+\,3 by subtracting 3 from both sides:

2x=82x = 8

Now undo the multiplication by dividing both sides by 2:

x=4x = 4

Worked example 2

x3−5=1\frac{x}{3} - 5 = 1

Undo − 5-\,5 first by adding 5 to both sides:

x3=6\frac{x}{3} = 6

Then undo the division by multiplying both sides by 3:

x=18x = 18

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

2x+1=72x + 1 = 7

Problem 2

3x−2=103x - 2 = 10

Problem 3

x2+1=5\frac{x}{2} + 1 = 5

Problem 4

x2−3=0\frac{x}{2} - 3 = 0

Practice

Standard problems matching the lesson.

Problem 5

2x+5=132x + 5 = 13

Problem 6

3x−4=143x - 4 = 14

Problem 7

4x+1=94x + 1 = 9

Problem 8

5x−8=125x - 8 = 12

Problem 9

x2+3=7\frac{x}{2} + 3 = 7

Problem 10

x3−1=4\frac{x}{3} - 1 = 4

Problem 11

6x+7=−56x + 7 = -5

Problem 12

−2x+9=1-2x + 9 = 1

Problem 13

10−x=310 - x = 3

Problem 14

2x−5=−112x - 5 = -11

Problem 15

x4+2=−1\frac{x}{4} + 2 = -1

Problem 16

7=3x+17 = 3x + 1

Challenge

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

Problem 17

−3x+8=−7-3x + 8 = -7

Problem 18

4x−9=−254x - 9 = -25

Problem 19

x5+7=4\frac{x}{5} + 7 = 4

Problem 20

−2x−5=7-2x - 5 = 7

Problem 21

−1=5x−11-1 = 5x - 11

Problem 22

x−3+2=6\frac{x}{-3} + 2 = 6