Comprehensive algebra worksheet designed to help students master solving linear equations without using negative numbers.

Here are the solutions to the linear equations, explained step by step:

Section A

1. $3x + 11 = 23$
- Subtract 11 from both sides: $3x = 12$
- Divide by 3: $x = 4$

2. $4x + 8 = 32$
- Subtract 8 from both sides: $4x = 24$
- Divide by 4: $x = 6$

3. $7x - 9 = 12$
- Add 9 to both sides: $7x = 21$
- Divide by 7: $x = 3$

4. $4x - 11 = 37$
- Add 11 to both sides: $4x = 48$
- Divide by 4: $x = 12$

5. $6x + 7 = 55$
- Subtract 7 from both sides: $6x = 48$
- Divide by 6: $x = 8$

6. $9x - 3 = 42$
- Add 3 to both sides: $9x = 45$
- Divide by 9: $x = 5$

7. $4x + 10 = 12$
- Subtract 10 from both sides: $4x = 2$
- Divide by 4: $x = \frac{2}{4} = 0.5$

8. $8x - 1 = 1$
- Add 1 to both sides: $8x = 2$
- Divide by 8: $x = \frac{2}{8} = 0.25$

9. $48x - 7 = 9$
- Add 7 to both sides: $48x = 16$
- Divide by 48: $x = \frac{16}{48} = \frac{1}{3}$

Section B

1. $2(x + 7) = 30$
- Divide both sides by 2: $x + 7 = 15$
- Subtract 7: $x = 8$

2. $3(x + 5) = 27$
- Divide both sides by 3: $x + 5 = 9$
- Subtract 5: $x = 4$

3. $5(x - 9) = 55$
- Divide both sides by 5: $x - 9 = 11$
- Add 9: $x = 20$

4. $4(3x + 6) = 48$
- Divide both sides by 4: $3x + 6 = 12$
- Subtract 6: $3x = 6$
- Divide by 3: $x = 2$

5. $7(4x - 12) = 56$
- Divide both sides by 7: $4x - 12 = 8$
- Add 12: $4x = 20$
- Divide by 4: $x = 5$

6. $2(8x - 60) = 24$
- Divide both sides by 2: $8x - 60 = 12$
- Add 60: $8x = 72$
- Divide by 8: $x = 9$

7. $2(4x + 22) = 48$
- Divide both sides by 2: $4x + 22 = 24$
- Subtract 22: $4x = 2$
- Divide by 4: $x = 0.5$

8. $9(12x + 4) = 72$
- Divide both sides by 9: $12x + 4 = 8$
- Subtract 4: $12x = 4$
- Divide by 12: $x = \frac{4}{12} = \frac{1}{3}$

9. $12(30x - 3) = 36$
- Divide both sides by 12: $30x - 3 = 3$
- Add 3: $30x = 6$
- Divide by 30: $x = \frac{6}{30} = 0.2$

Section C

1. $x + 8 = 9x$
- Subtract $x$ from both sides: $8 = 8x$
- Divide by 8: $x = 1$

2. $30 + x = 7x$
- Subtract $x$ from both sides: $30 = 6x$
- Divide by 6: $x = 5$

3. $2x + 16 = 6x$
- Subtract $2x$ from both sides: $16 = 4x$
- Divide by 4: $x = 4$

4. $96 - 5x = 7x$
- Add $5x$ to both sides: $96 = 12x$
- Divide by 12: $x = 8$

5. $70 - 6x = 4x$
- Add $6x$ to both sides: $70 = 10x$
- Divide by 10: $x = 7$

6. $132 - 9x = 3x$
- Add $9x$ to both sides: $132 = 12x$
- Divide by 12: $x = 11$

7. $6(x + 5) = 8x$
- Distribute: $6x + 30 = 8x$
- Subtract $6x$ from both sides: $30 = 2x$
- Divide by 2: $x = 15$

8. $6(12 - 3x) = 6x$
- Distribute: $72 - 18x = 6x$
- Add $18x$ to both sides: $72 = 24x$
- Divide by 24: $x = 3$

9. $4(1 - 2x) = 12x$
- Distribute: $4 - 8x = 12x$
- Add $8x$ to both sides: $4 = 20x$
- Divide by 20: $x = 0.2$

Section D

1. $9x - 2 = 2x + 12$
- Subtract $2x$ from both sides: $7x - 2 = 12$
- Add 2: $7x = 14$
- Divide by 7: $x = 2$

2. $12x + 4 = 31 + 3x$
- Subtract $3x$ from both sides: $9x + 4 = 31$
- Subtract 4: $9x = 27$
- Divide by 9: $x = 3$

3. $46 + 3x = 8x - 14$
- Subtract $3x$ from both sides: $46 = 5x - 14$
- Add 14: $60 = 5x$
- Divide by 5: $x = 12$

4. $87 + 2x = 6 + 11x$
- Subtract $2x$ from both sides: $87 = 6 + 9x$
- Subtract 6: $81 = 9x$
- Divide by 9: $x = 9$

5. $14x - 23 = 2x + 1$
- Subtract $2x$ from both sides: $12x - 23 = 1$
- Add 23: $12x = 24$
- Divide by 12: $x = 2$

6. $5x - 6 = 48 - 13x$
- Add $13x$ to both sides: $18x - 6 = 48$
- Add 6: $18x = 54$
- Divide by 18: $x = 3$

7. $69 - 15x = 24 - 6x$
- Add $15x$ to both sides: $69 = 24 + 9x$
- Subtract 24: $45 = 9x$
- Divide by 9: $x = 5$

8. $8x - 21 = 86 - 2x$
- Add $2x$ to both sides: $10x - 21 = 86$
- Add 21: $10x = 107$
- Divide by 10: $x = 10.7$

9. $16x + 13 = 22x - 77$
- Subtract $16x$ from both sides: $13 = 6x - 77$
- Add 77: $90 = 6x$
- Divide by 6: $x = 15$