Printable math worksheet for solving linear equations, divided into three sections with varying levels of complexity.

Let’s solve each equation step by step. We’ll go section by section, and for each problem, we’ll isolate the variable (usually x) using inverse operations — like adding/subtracting first, then multiplying/dividing.

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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 or 1/2

7) 5 + 10x = -15
Subtract 5:
10x = -20
Divide by 10:
x = -2

8) 10 = 7 – x
Subtract 7:
3 = -x
Multiply both sides 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 = 1/5 or 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 both sides 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 both sides 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 = 11/5 = 2.2
Add 3:
4x = 5.2
Divide by 4:
x = 1.3 or 13/10

Wait — let’s do it with fractions to be exact:

5(4x – 3) = 11
→ 20x – 15 = 11
→ 20x = 26
→ x = 26/20 = 13/10 → same as 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: 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
Distribute the -2:
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
10) 7
11) 5
12) -4