Robinson Tuition
Year 9 · Key Stage 3 · free KS3 maths worksheet

Solving equations

12 original questions, 38 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1
  1. Write down the inverse of each operation.
    (i)  add 7     (ii)  multiply by 4     (iii)  divide by 3
  2. Mia thinks of a number. She multiplies it by 3 and then adds 8. Her answer is 29.
    Use inverse operations to work out Mia's number.
3 marks
Show answer
a) subtract 7, divide by 4, multiply by 3 b) 7
2
  1. Solve  p + 9 = 4
  2. Solve  5q = −30
  3. Solve  r − 3 = −10
3 marks
Show answer
a) p = -5 b) q = -6 c) r = -7
3

Solve 5x − 7 = 23

2 marks
Show answer
x = 6
4
  1. Make x the subject of  y = x + 9
  2. Make a the subject of  P = 4a
  3. Make m the subject of  k = 3m − 2
3 marks
Show answer
a) x = y - 9 b) a = P/4 c) m = (k + 2)/3
5

Solve 3(x + 4) = 27

2 marks
Show answer
x = 5
6

Solve

  1. 5(2x − 3) = 25
  2. 4(x + 6) = 10
3 marks
Show answer
a) x = 4 b) x = -3.5
7

Priya thinks of a number.

She multiplies the number by 4 and then subtracts 9.

Her answer is 35.

Work out the number Priya thought of.

3 marks
Show answer
11
8

Ollie buys 4 cinema tickets and one large popcorn.

Each ticket costs £t. The popcorn costs £6.

He pays £38 altogether.

  1. Write an equation in t.
  2. Solve your equation to find the cost of one ticket.
3 marks
Show answer
a) 4t + 6 = 38 b) £8
9

Solve 7x − 5 = 3x + 23

3 marks
Show answer
x = 7
10

Solve

  1. 3(2x − 1) = 4x + 9
  2. 8 − 3x = 2x − 12
4 marks
Show answer
a) x = 6 b) x = 4
11

Amira and Josh collect football stickers. Every packet has the same number of stickers, n.

Amira has 5 full packets and 3 loose stickers.
Josh has 3 full packets and 19 loose stickers.

Amira and Josh have the same number of stickers.

Work out how many stickers Amira has.

4 marks
Show answer
43
12

A rectangle has length (2x + 5) cm and width (x + 2) cm.

The perimeter of the rectangle is 38 cm.

Work out the area of the rectangle.

5 marks
Show answer
78 cm2

Your score

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Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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