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Grade 8 Math — Linear equations with the unknown on both sides

Solve equations that have the unknown on both sides, and use them to answer word problems.

Name: ________________________

Before you start

The scale is level, and there is a mystery box on each side. Move the weights about and find out what keeps it level and what tips it over.

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Lift one box off each side and the beam does not move at all. That is what “take the unknown off both sides” means, and it is why the boxes on the two sides can be gathered into one.

  1. 1.Match each equation to its solution.

    • 2x + 3 = 11
    • 3x - 1 = 14
    • 5x + 4 = 4x + 10
    • 7x = 4x + 21
    • 2x - 9 = x - 1
    • 7
    • 8
    • 4
    • 6
    • 5

  2. 2.A rectangle is 3 inches longer than it is wide, and its perimeter is 26 inches. How wide is it, in inches? Give just the number.

  3. 3.Solve x/5 + 2 = 5. x = ?

  4. 4.Solve (x + 4)/3 = 2. x = ?

  5. 5.Why may the same number be taken away from both sides of an equation?

    • a) Because taking away always makes an equation simpler
    • b) Because the two sides stay equal if you do the same thing to each
    • c) Because the left side is always the more important one
    • d) Because the unknown must end up on the left

  6. 6.Put these equations in order by their solution, smallest x first.

    • 2x + 1 = x + 2
    • 5x + 2 = 3x + 18
    • x - 4 = 6
    • 3x = x + 6
    • 4x - 5 = 2x + 5

  7. 7.Solve 4(x - 3) = 2x + 6. x = ?

  8. 8.Solve 3x + 5 = 2x + 11. x = ?

Answer key — Grade 8 Math — Linear equations with the unknown on both sides

  1. 1. 2x + 3 = 11 → 4; 3x - 1 = 14 → 5; 5x + 4 = 4x + 10 → 6; 7x = 4x + 21 → 7; 2x - 9 = x - 1 → 8
  2. 2. 5
  3. 3. 15
  4. 4. 2
  5. 5. b) Because the two sides stay equal if you do the same thing to each
  6. 6. 1. 2x + 1 = x + 2 2. 3x = x + 6 3. 4x - 5 = 2x + 5 4. 5x + 2 = 3x + 18 5. x - 4 = 6
  7. 7. 9
  8. 8. 6