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Year 9 Maths — 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.Solve 4(x - 3) = 2x + 6. x = ?

  2. 2.Solve 5x - 4 = 3x + 10. x = ?

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

  4. 4.Solve 7 - 2x = x + 1. x = ?

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

  6. 6.Which value of x makes 6x - 5 = 4x + 3 true?

    • a) 1
    • b) -4
    • c) 2
    • d) 4

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

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

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

Answer key — Year 9 Maths — Linear equations with the unknown on both sides

  1. 1. 9
  2. 2. 7
  3. 3. 2
  4. 4. 2
  5. 5. 5
  6. 6. d) 4
  7. 7. 1. 2x + 1 = x + 2 2. 3x = x + 6 3. 4x - 5 = 2x + 5 4. 5x + 2 = 3x + 18 5. x - 4 = 6
  8. 8. 15