Solving Linear Equations worksheet with sections A, B, and C for practicing algebraic problem-solving.

Let’s solve each equation step by step. We’ll isolate the variable x on one side of the equation by doing the same thing to both sides — like subtracting, adding, or dividing.

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Section A

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

2) 5x + 7 = 42
→ Subtract 7: 5x = 35
→ Divide by 5: x = 7

3) 4x + 3 = 51
→ Subtract 3: 4x = 48
→ Divide by 4: x = 12

4) 9x + 5 = 41
→ Subtract 5: 9x = 36
→ Divide by 9: x = 4

5) 4x + 2 = 34
→ Subtract 2: 4x = 32
→ Divide by 4: x = 8

6) 11x + 3 = 36
→ Subtract 3: 11x = 33
→ Divide by 11: x = 3

7) 10x + 2 = 72
→ Subtract 2: 10x = 70
→ Divide by 10: x = 7

8) 7x + 3 = 52
→ Subtract 3: 7x = 49
→ Divide by 7: x = 7

9) 6x + 5 = 17
→ Subtract 5: 6x = 12
→ Divide by 6: x = 2

10) 4x + 7 = 9
→ Subtract 7: 4x = 2
→ Divide by 4: x = 0.5 (or ½)

11) 8x + 11 = 15
→ Subtract 11: 8x = 4
→ Divide by 8: x = 0.5 (or ½)

12) 4x + 17 = 18
→ Subtract 17: 4x = 1
→ Divide by 4: x = 0.25 (or ¼)

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Section B

1) 1 + 6x = 19
→ Subtract 1: 6x = 18
→ Divide by 6: x = 3

2) 9 + 7x = 30
→ Subtract 9: 7x = 21
→ Divide by 7: x = 3

3) 3 + 2x = 17
→ Subtract 3: 2x = 14
→ Divide by 2: x = 7

4) 11 + 5x = 71
→ Subtract 11: 5x = 60
→ Divide by 5: x = 12

5) 5 + 3x = 32
→ Subtract 5: 3x = 27
→ Divide by 3: x = 9

6) 4 + 5x = 44
→ Subtract 4: 5x = 40
→ Divide by 5: x = 8

7) 23 = x + 8
→ Subtract 8: 15 = x → x = 15

8) 28 = 3x + 1
→ Subtract 1: 27 = 3x
→ Divide by 3: x = 9

9) 53 = 8x + 5
→ Subtract 5: 48 = 8x
→ Divide by 8: x = 6

10) 13 = 11 + 4x
→ Subtract 11: 2 = 4x
→ Divide by 4: x = 0.5 (or ½)

11) 7 = 8x + 3
→ Subtract 3: 4 = 8x
→ Divide by 8: x = 0.5 (or ½)

12) 12 = 7 + 15x
→ Subtract 7: 5 = 15x
→ Divide by 15: x = ⅓ (or about 0.333)

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Section C

1) 4x – 1 = 31
→ Add 1: 4x = 32
→ Divide by 4: x = 8

2) 3x – 4 = 29
→ Add 4: 3x = 33
→ Divide by 3: x = 11

3) 6x – 5 = 31
→ Add 5: 6x = 36
→ Divide by 6: x = 6

4) 8x – 2 = 46
→ Add 2: 8x = 48
→ Divide by 8: x = 6

5) 2x – 7 = 21
→ Add 7: 2x = 28
→ Divide by 2: x = 14

6) 7x – 3 = 18
→ Add 3: 7x = 21
→ Divide by 7: x = 3

7) 9x – 4 = 32
→ Add 4: 9x = 36
→ Divide by 9: x = 4

8) 5x – 1 = 64
→ Add 1: 5x = 65
→ Divide by 5: x = 13

9) 12x – 9 = 39
→ Add 9: 12x = 48
→ Divide by 12: x = 4

10) 2x – 1 = 2
→ Add 1: 2x = 3
→ Divide by 2: x = 1.5 (or ³⁄₂)

11) 4x – 8 = 10
→ Add 8: 4x = 18
→ Divide by 4: x = 4.5 (or ⁹⁄₂)

12) 15x – 2 = 3
→ Add 2: 15x = 5
→ Divide by 15: x = ⅓ (or about 0.333)

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Final Answer:
Section A:
1) 2
2) 7
3) 12
4) 4
5) 8
6) 3
7) 7
8) 7
9) 2
10) 0.5
11) 0.5
12) 0.25

Section B:
1) 3
2) 3
3) 7
4) 12
5) 9
6) 8
7) 15
8) 9
9) 6
10) 0.5
11) 0.5
12) ⅓

Section C:
1) 8
2) 11
3) 6
4) 6
5) 14
6) 3
7) 4
8) 13
9) 4
10) 1.5
11) 4.5
12) ⅓