Math worksheet for solving linear equations, divided into three sections with problems and space for answers.

Here are the solutions for each section of the worksheet. I have solved them step-by-step to ensure accuracy.

Section A

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

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

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

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

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

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

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

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

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

10) $4x + 7 = 9$
- Subtract 7 from both sides: $4x = 2$
- Divide by 4: $x = 0.5$ (or $\frac{1}{2}$)

11) $8x + 11 = 15$
- Subtract 11 from both sides: $8x = 4$
- Divide by 8: $x = 0.5$ (or $\frac{1}{2}$)

12) $4x + 17 = 18$
- Subtract 17 from both sides: $4x = 1$
- Divide by 4: $x = 0.25$ (or $\frac{1}{4}$)

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Section B

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

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

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

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

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

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

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

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

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

10) $13 = 11 + 4x$
- Subtract 11 from both sides: $2 = 4x$
- Divide by 4: $0.5 = x$
- So, $x = 0.5$ (or $\frac{1}{2}$)

11) $7 = 8x + 3$
- Subtract 3 from both sides: $4 = 8x$
- Divide by 8: $0.5 = x$
- So, $x = 0.5$ (or $\frac{1}{2}$)

12) $12 = 7 + 15x$
- Subtract 7 from both sides: $5 = 15x$
- Divide by 15: $\frac{5}{15} = x$
- Simplify fraction: $x = \frac{1}{3}$

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Section C

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

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

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

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

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

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

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

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

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

10) $2x - 1 = 2$
- Add 1 to both sides: $2x = 3$
- Divide by 2: $x = 1.5$ (or $\frac{3}{2}$ or $1\frac{1}{2}$)

11) $4x - 8 = 10$
- Add 8 to both sides: $4x = 18$
- Divide by 4: $x = 4.5$ (or $\frac{9}{2}$ or $4\frac{1}{2}$)

12) $15x - 2 = 3$
- Add 2 to both sides: $15x = 5$
- Divide by 15: $x = \frac{5}{15}$
- Simplify fraction: $x = \frac{1}{3}$

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) 1/3

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) 1/3