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Pre-Algebra

Solving Multi-Step Equations

Lesson

A multi-step equationneeds more than two operations to solve. The strategy combines everything you’ve learned: distribute if needed, combine like terms on each side, then undo operations in reverse order to isolate xx.

A reliable order of attack:

  1. Distribute any factors across parentheses.
  2. Combine like terms on each side of the equation.
  3. Undo addition or subtraction first to get the variable term alone.
  4. Undo multiplication or division to get xx by itself.

Worked example 1

2(x+3)+4=182(x + 3) + 4 = 18

Distribute the 2:

2x+6+4=182x + 6 + 4 = 18

Combine like terms on the left:

2x+10=182x + 10 = 18

Subtract 10:

2x=82x = 8

Divide by 2:

x=4x = 4

Worked example 2

5x−3+2x=255x - 3 + 2x = 25

Combine like terms on the left (no distribution needed):

7x−3=257x - 3 = 25

Add 3:

7x=287x = 28

Divide by 7:

x=4x = 4

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

x+x=6x + x = 6

Problem 2

2x+x=92x + x = 9

Problem 3

4x−x=124x - x = 12

Problem 4

x+2+x=8x + 2 + x = 8

Practice

Standard problems matching the lesson.

Problem 5

3x+2x=203x + 2x = 20

Problem 6

2x+5+x=172x + 5 + x = 17

Problem 7

5x−2x+4=195x - 2x + 4 = 19

Problem 8

2(x+4)=142(x + 4) = 14

Problem 9

3(x−2)=93(x - 2) = 9

Problem 10

4(x+1)−2=184(x + 1) - 2 = 18

Problem 11

2(2x−1)=142(2x - 1) = 14

Problem 12

5(x−3)+2x=65(x - 3) + 2x = 6

Problem 13

3x−4+x=163x - 4 + x = 16

Problem 14

−2(x+5)=−16-2(x + 5) = -16

Problem 15

6+3(x−2)=96 + 3(x - 2) = 9

Problem 16

4x−2(x+3)=44x - 2(x + 3) = 4

Challenge

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

Problem 17

5(x−1)−2x=75(x - 1) - 2x = 7

Problem 18

3+2(x+4)=173 + 2(x + 4) = 17

Problem 19

−3(x+2)+4x=5-3(x + 2) + 4x = 5

Problem 20

6(2x−1)−5x=226(2x - 1) - 5x = 22

Problem 21

4x+3(x−2)=224x + 3(x - 2) = 22

Problem 22

−2(3x+1)+5x=−10-2(3x + 1) + 5x = -10