Math worksheet for solving linear equations, divided into three sections with problems of increasing complexity, designed for GCSE Foundation level students.

Explanation:
Let's solve each equation step by step. The goal is to find the value of x in each equation. We do this by getting x by itself on one side of the equation.

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Section A

1) 7x + 9 = 23
Subtract 9 from both sides:
7x = 23 - 9
7x = 14
Divide both sides by 7:
x = 14 ÷ 7
x = 2

2) 5x + 7 = 42
Subtract 7 from both sides:
5x = 42 - 7
5x = 35
Divide both sides by 5:
x = 35 ÷ 5
x = 7

3) 4x + 3 = 51
Subtract 3 from both sides:
4x = 51 - 3
4x = 48
Divide both sides by 4:
x = 48 ÷ 4
x = 12

4) 9x + 5 = 41
Subtract 5 from both sides:
9x = 41 - 5
9x = 36
Divide both sides by 9:
x = 36 ÷ 9
x = 4

5) 4x + 2 = 34
Subtract 2 from both sides:
4x = 34 - 2
4x = 32
Divide both sides by 4:
x = 32 ÷ 4
x = 8

6) 11x + 3 = 36
Subtract 3 from both sides:
11x = 36 - 3
11x = 33
Divide both sides by 11:
x = 33 ÷ 11
x = 3

7) 10x + 2 = 72
Subtract 2 from both sides:
10x = 72 - 2
10x = 70
Divide both sides by 10:
x = 70 ÷ 10
x = 7

8) 7x + 3 = 52
Subtract 3 from both sides:
7x = 52 - 3
7x = 49
Divide both sides by 7:
x = 49 ÷ 7
x = 7

9) 6x + 5 = 17
Subtract 5 from both sides:
6x = 17 - 5
6x = 12
Divide both sides by 6:
x = 12 ÷ 6
x = 2

10) 4x + 7 = 9
Subtract 7 from both sides:
4x = 9 - 7
4x = 2
Divide both sides by 4:
x = 2 ÷ 4
x = 0.5

11) 8x + 11 = 15
Subtract 11 from both sides:
8x = 15 - 11
8x = 4
Divide both sides by 8:
x = 4 ÷ 8
x = 0.5

12) 4x + 17 = 18
Subtract 17 from both sides:
4x = 18 - 17
4x = 1
Divide both sides by 4:
x = 1 ÷ 4
x = 0.25

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Section B

1) 1 + 6x = 19
Subtract 1 from both sides:
6x = 19 - 1
6x = 18
Divide both sides by 6:
x = 18 ÷ 6
x = 3

2) 9 + 7x = 30
Subtract 9 from both sides:
7x = 30 - 9
7x = 21
Divide both sides by 7:
x = 21 ÷ 7
x = 3

3) 3 + 2x = 17
Subtract 3 from both sides:
2x = 17 - 3
2x = 14
Divide both sides by 2:
x = 14 ÷ 2
x = 7

4) 11 + 5x = 71
Subtract 11 from both sides:
5x = 71 - 11
5x = 60
Divide both sides by 5:
x = 60 ÷ 5
x = 12

5) 5 + 3x = 32
Subtract 5 from both sides:
3x = 32 - 5
3x = 27
Divide both sides by 3:
x = 27 ÷ 3
x = 9

6) 4 + 5x = 44
Subtract 4 from both sides:
5x = 44 - 4
5x = 40
Divide both sides by 5:
x = 40 ÷ 5
x = 8

7) 23 = x + 8
Subtract 8 from both sides:
23 - 8 = x
15 = x
x = 15

8) 28 = 3x + 1
Subtract 1 from both sides:
28 - 1 = 3x
27 = 3x
Divide both sides by 3:
x = 27 ÷ 3
x = 9

9) 53 = 8x + 5
Subtract 5 from both sides:
53 - 5 = 8x
48 = 8x
Divide both sides by 8:
x = 48 ÷ 8
x = 6

10) 13 = 11 + 4x
Subtract 11 from both sides:
13 - 11 = 4x
2 = 4x
Divide both sides by 4:
x = 2 ÷ 4
x = 0.5

11) 7 = 8x + 3
Subtract 3 from both sides:
7 - 3 = 8x
4 = 8x
Divide both sides by 8:
x = 4 ÷ 8
x = 0.5

12) 12 = 7 + 15x
Subtract 7 from both sides:
12 - 7 = 15x
5 = 15x
Divide both sides by 15:
x = 5 ÷ 15
x = 1/3 (or 0.333...)

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Section C

1) 4x - 1 = 31
Add 1 to both sides:
4x = 31 + 1
4x = 32
Divide both sides by 4:
x = 32 ÷ 4
x = 8

2) 3x - 4 = 29
Add 4 to both sides:
3x = 29 + 4
3x = 33
Divide both sides by 3:
x = 33 ÷ 3
x = 11

3) 6x - 5 = 31
Add 5 to both sides:
6x = 31 + 5
6x = 36
Divide both sides by 6:
x = 36 ÷ 6
x = 6

4) 8x - 2 = 46
Add 2 to both sides:
8x = 46 + 2
8x = 48
Divide both sides by 8:
x = 48 ÷ 8
x = 6

5) 2x - 7 = 21
Add 7 to both sides:
2x = 21 + 7
2x = 28
Divide both sides by 2:
x = 28 ÷ 2
x = 14

6) 7x - 3 = 18
Add 3 to both sides:
7x = 18 + 3
7x = 21
Divide both sides by 7:
x = 21 ÷ 7
x = 3

7) 9x - 4 = 32
Add 4 to both sides:
9x = 32 + 4
9x = 36
Divide both sides by 9:
x = 36 ÷ 9
x = 4

8) 5x - 1 = 64
Add 1 to both sides:
5x = 64 + 1
5x = 65
Divide both sides by 5:
x = 65 ÷ 5
x = 13

9) 12x - 9 = 39
Add 9 to both sides:
12x = 39 + 9
12x = 48
Divide both sides by 12:
x = 48 ÷ 12
x = 4

10) 2x - 1 = 2
Add 1 to both sides:
2x = 2 + 1
2x = 3
Divide both sides by 2:
x = 3 ÷ 2
x = 1.5

11) 4x - 8 = 10
Add 8 to both sides:
4x = 10 + 8
4x = 18
Divide both sides by 4:
x = 18 ÷ 4
x = 4.5

12) 15x - 2 = 3
Add 2 to both sides:
15x = 3 + 2
15x = 5
Divide both sides by 15:
x = 5 ÷ 15
x = 1/3 (or 0.333...)

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Final Answer:
The solutions are:

Section A
1) x = 2
2) x = 7
3) x = 12
4) x = 4
5) x = 8
6) x = 3
7) x = 7
8) x = 7
9) x = 2
10) x = 0.5
11) x = 0.5
12) x = 0.25

Section B
1) x = 3
2) x = 3
3) x = 7
4) x = 12
5) x = 9
6) x = 8
7) x = 15
8) x = 9
9) x = 6
10) x = 0.5
11) x = 0.5
12) x = 1/3

Section C
1) x = 8
2) x = 11
3) x = 6
4) x = 6
5) x = 14
6) x = 3
7) x = 4
8) x = 13
9) x = 4
10) x = 1.5
11) x = 4.5
12) x = 1/3