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Grade 4 · Foundation and Higher · free GCSE maths worksheet

Solving equations with the unknown on both sides

Collecting terms on one side.

11 original questions, 37 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Solve 4x + 3 = x + 18

2 marks
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x = 5
2

Solve 5x − 8 = 2x + 10

3 marks
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x = 6
3

Solve 7x − 5 = 3x + 23

3 marks
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x = 7
4

Solve 2x + 9 = 5x + 21

3 marks
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x = -4
5

Solve 5(x − 2) = 3x + 8

3 marks
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x = 9
6

Solve 4x + 13 = x + 3

3 marks
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x = 8
7

Sam and Tia each think of the same number.

Sam multiplies his number by 4 and then subtracts 7.

Tia multiplies her number by 2 and then adds 9.

They both get the same answer. Work out their number.

3 marks
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8
8
  1. Solve 2(3x + 4) = 5x + 17
  2. Factorise fully 6y2 + 9y
4 marks
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a) x = 9 b) 3y(2y + 3)
9
  1. Solve 9 − 2x = 3(x − 7)
  2. Simplify (m5)2 ÷ m3
4 marks
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a) x = 6 b) m7
10
  1. Simplify 4a + 3b − a + 5b
  2. Solve 5x − 42 = 18
  3. Solve 4(y + 3) = 2y + 22
5 marks
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a) 3a + 8b b) x = 8 c) y = 5
11

A square has sides of length (3x + 2) cm. A regular pentagon has sides of length (x + 10) cm.

The square and the pentagon have the same perimeter.

Work out the length of one side of the square.

4 marks
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20

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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