Year 8 Maths Worksheets | Free Printable PDF Year 8 Worksheets - Free Printable

I will solve all the linear equations from the worksheet provided, going section by section.

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## SECTION A

1) 4x + 10 = 30

Subtract 10 from both sides:
4x = 20
Divide by 4:
x = 5 ✔

2) 4x – 8 = 20

Add 8 to both sides:
4x = 28
Divide by 4:
x = 7 ✔

3) 5 + 2x = 65

Subtract 5:
2x = 60
Divide by 2:
x = 30 ✔

4) 9 + 4x = -15

Subtract 9:
4x = -24
Divide by 4:
x = -6 ✔

5) 14 + 6x = 2

Subtract 14:
6x = -12
Divide by 6:
x = -2 ✔

6) 2x – 3 = -2

Add 3:
2x = 1
Divide by 2:
x = 0.5 ✔

7) 5 + 10x = -15

Subtract 5:
10x = -20
Divide by 10:
x = -2 ✔

8) 10 = 7 – x

Subtract 7:
3 = -x
Multiply by -1:
x = -3 ✔

9) -3 = 16 – x

Subtract 16:
-19 = -x
Multiply by -1:
x = 19 ✔

10) -4 = 12 – 2x

Subtract 12:
-16 = -2x
Divide by -2:
x = 8 ✔

11) 25 = 46 – 3x

Subtract 46:
-21 = -3x
Divide by -3:
x = 7 ✔

12) 8 = 9 – 5x

Subtract 9:
-1 = -5x
Divide by -5:
x = 0.2 ✔

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## SECTION B

1) x/2 + 11 = 19

Subtract 11:
x/2 = 8
Multiply by 2:
x = 16 ✔

2) x/7 – 6 = 1

Add 6:
x/7 = 7
Multiply by 7:
x = 49 ✔

3) 12 + x/5 = 20

Subtract 12:
x/5 = 8
Multiply by 5:
x = 40 ✔

4) 3 = x/4 – 3

Add 3:
6 = x/4
Multiply by 4:
x = 24 ✔

5) 7 = x/2 – 4

Add 4:
11 = x/2
Multiply by 2:
x = 22 ✔

6) -2 = x/8 – 5

Add 5:
3 = x/8
Multiply by 8:
x = 24 ✔

7) -1 = 6 + x/2

Subtract 6:
-7 = x/2
Multiply by 2:
x = -14 ✔

8) 14 – x/3 = 10

Subtract 14:
-x/3 = -4
Multiply by -3:
x = 12 ✔

9) 5 – x/9 = -1

Subtract 5:
-x/9 = -6
Multiply by -9:
x = 54 ✔

10) (x + 5)/3 = 12

Multiply by 3:
x + 5 = 36
Subtract 5:
x = 31 ✔

11) (x – 4)/11 = 9

Multiply by 11:
x – 4 = 99
Add 4:
x = 103 ✔

12) (x + 3)/8 = -2

Multiply by 8:
x + 3 = -16
Subtract 3:
x = -19 ✔

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## SECTION C

1) 3(x + 2) = 15

Divide by 3:
x + 2 = 5
Subtract 2:
x = 3 ✔

2) 2(x + 5) = 24

Divide by 2:
x + 5 = 12
Subtract 5:
x = 7 ✔

3) 6(x – 9) = 12

Divide by 6:
x – 9 = 2
Add 9:
x = 11 ✔

4) 2(3x + 5) = -44

Divide by 2:
3x + 5 = -22
Subtract 5:
3x = -27
Divide by 3:
x = -9 ✔

5) 5(4x – 3) = 11

Divide by 5:
4x – 3 = 2.2
Add 3:
4x = 5.2
Divide by 4:
x = 1.3 ✔

6) -3(2x + 1) = 21

Divide by -3:
2x + 1 = -7
Subtract 1:
2x = -8
Divide by 2:
x = -4 ✔

7) -9(x – 4) = 54

Divide by -9:
x – 4 = -6
Add 4:
x = -2 ✔

8) 7(x – 4) – 3 = 46

Add 3:
7(x – 4) = 49
Divide by 7:
x – 4 = 7
Add 4:
x = 11 ✔

9) 2(3x – 1) + 3 = 21

Subtract 3:
2(3x – 1) = 18
Divide by 2:
3x – 1 = 9
Add 1:
3x = 10
Divide by 3:
x = 10/3 ≈ 3.333... ✔

10) 2(x + 1) + 3x = 37

Expand:
2x + 2 + 3x = 37
Combine like terms:
5x + 2 = 37
Subtract 2:
5x = 35
Divide by 5:
x = 7 ✔

11) 12 + 4(2x + 4) = 68

Subtract 12:
4(2x + 4) = 56
Divide by 4:
2x + 4 = 14
Subtract 4:
2x = 10
Divide by 2:
x = 5 ✔

12) 3x – 2(6x – 3) = 42

Expand:
3x – 12x + 6 = 42
Combine:
-9x + 6 = 42
Subtract 6:
-9x = 36
Divide by -9:
x = -4 ✔

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Final Answer:
Section A:
1) 5
2) 7
3) 30
4) -6
5) -2
6) 0.5
7) -2
8) -3
9) 19
10) 8
11) 7
12) 0.2

Section B:
1) 16
2) 49
3) 40
4) 24
5) 22
6) 24
7) -14
8) 12
9) 54
10) 31
11) 103
12) -19

Section C:
1) 3
2) 7
3) 11
4) -9
5) 1.3
6) -4
7) -2
8) 11
9) 10/3 or 3.333...
10) 7
11) 5
12) -4