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Pre-Algebra

Equations with Variables on Both Sides

Lesson

Sometimes the variable shows up on both sidesof the equation. The new move: get the variable terms onto the same side first by adding or subtracting one of them from both sides. Then it’s a regular multi-step equation.

A reliable order of attack:

  1. Distribute and combine like terms on each side, if needed.
  2. Move all variable terms to one side (usually the side that ends up positive), and all constants to the other.
  3. Solve the remaining one- or two-step equation.

Worked example 1

3x+5=2x+93x + 5 = 2x + 9

Subtract 2x2x from both sides to gather the variable terms on the left:

x+5=9x + 5 = 9

Subtract 5:

x=4x = 4

Worked example 2

6x−4=2x+86x - 4 = 2x + 8

Subtract 2x2x from both sides:

4x−4=84x - 4 = 8

Add 4:

4x=124x = 12

Divide by 4:

x=3x = 3

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

2x=x+52x = x + 5

Problem 2

4x=3x+74x = 3x + 7

Problem 3

x+6=2xx + 6 = 2x

Problem 4

5x=2x+95x = 2x + 9

Practice

Standard problems matching the lesson.

Problem 5

3x+5=2x+93x + 5 = 2x + 9

Problem 6

5x−2=3x+85x - 2 = 3x + 8

Problem 7

4x+1=2x+74x + 1 = 2x + 7

Problem 8

7x−3=4x+97x - 3 = 4x + 9

Problem 9

2x+6=5x−92x + 6 = 5x - 9

Problem 10

8x=3x+258x = 3x + 25

Problem 11

6x+4=4x+46x + 4 = 4x + 4

Problem 12

9x−7=5x+139x - 7 = 5x + 13

Problem 13

10−x=3x+210 - x = 3x + 2

Problem 14

2(x+3)=x+112(x + 3) = x + 11

Problem 15

3(x−2)=x+43(x - 2) = x + 4

Problem 16

5x−1=2(x+4)5x - 1 = 2(x + 4)

Problem 17

30+15x=50+10x30 + 15x = 50 + 10x

Problem 18

40+5x=60+3x40 + 5x = 60 + 3x

Challenge

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

Problem 19

3(x+1)=5x−73(x + 1) = 5x - 7

Problem 20

4(x−2)=2(x+1)4(x - 2) = 2(x + 1)

Problem 21

−2(x−3)=x+9-2(x - 3) = x + 9

Problem 22

7x+3=4(x+6)7x + 3 = 4(x + 6)

Problem 23

4x−2(x+1)=x+44x - 2(x + 1) = x + 4

Problem 24

3(2x−1)=5x+43(2x - 1) = 5x + 4

Problem 25

30+0.10x=20+0.20x30 + 0.10x = 20 + 0.20x

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