Solving Linear Equations with the Distributive Property Worksheet ... - Free Printable

Here are the solutions for the linear equations on the worksheet.

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 from both sides: $2x = 60$
Divide by 2: $x = 30$

4) $9 + 4x = -15$
Subtract 9 from both sides: $4x = -24$
Divide by 4: $x = -6$

5) $14 + 6x = 2$
Subtract 14 from both sides: $6x = -12$
Divide by 6: $x = -2$

6) $2x - 3 = 2$
Add 3 to both sides: $2x = 5$
Divide by 2: $x = 2.5$ (or $\frac{5}{2}$)

7) $5 + 10x = -15$
Subtract 5 from both sides: $10x = -20$
Divide by 10: $x = -2$

8) $10 = 7 - x$
Subtract 7 from both sides: $3 = -x$
Multiply by -1: $x = -3$

9) $-x = 16 - x$
Add $x$ to both sides: $0 = 16$
This is impossible. No Solution

10) $4x = 12 - 2x$
Add $2x$ to both sides: $6x = 12$
Divide by 6: $x = 2$

11) $25 = 45 - 3x$
Subtract 45 from both sides: $-20 = -3x$
Divide by -3: $x = \frac{20}{3}$ (or $6.67$)

12) $8 = 9 - 5x$
Subtract 9 from both sides: $-1 = -5x$
Divide by -5: $x = 0.2$ (or $\frac{1}{5}$)

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Section B

1) $\frac{x}{2} + 11 = 19$
Subtract 11 from both sides: $\frac{x}{2} = 8$
Multiply by 2: $x = 16$

2) $\frac{x}{7} - 6 = 1$
Add 6 to both sides: $\frac{x}{7} = 7$
Multiply by 7: $x = 49$

3) $12 + \frac{x}{5} = 20$
Subtract 12 from both sides: $\frac{x}{5} = 8$
Multiply by 5: $x = 40$

4) $3 = \frac{x}{4} - 3$
Add 3 to both sides: $6 = \frac{x}{4}$
Multiply by 4: $x = 24$

5) $7 = \frac{x}{2} - 4$
Add 4 to both sides: $11 = \frac{x}{2}$
Multiply by 2: $x = 22$

6) $-2 = \frac{x}{5} - 5$
Add 5 to both sides: $3 = \frac{x}{5}$
Multiply by 5: $x = 15$

7) $-1 = 6 + \frac{x}{2}$
Subtract 6 from both sides: $-7 = \frac{x}{2}$
Multiply by 2: $x = -14$

8) $14 - \frac{x}{3} = 10$
Subtract 14 from both sides: $-\frac{x}{3} = -4$
Multiply by -3: $x = 12$

9) $-\frac{x}{2} - 5 = -1$
Add 5 to both sides: $-\frac{x}{2} = 4$
Multiply by -2: $x = -8$

10) $\frac{x + 5}{3} = 12$
Multiply by 3: $x + 5 = 36$
Subtract 5: $x = 31$

11) $\frac{x - 4}{4} = 9$
Multiply by 4: $x - 4 = 36$
Add 4: $x = 40$

12) $\frac{x + 3}{8} = -2$
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) $(4x - 3) = 11$
Add 3: $4x = 14$
Divide by 4: $x = 3.5$ (or $\frac{7}{2}$)

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: $x = \frac{10}{3}$ (or $3.33$)

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) $3x - 2(3x - 3) = 42$
Expand brackets (watch the negative sign): $3x - 6x + 6 = 42$
Combine like terms: $-3x + 6 = 42$
Subtract 6: $-3x = 36$
Divide by -3: $x = -12$

Final Answer:
See the step-by-step solutions above for all problems in Sections A, B, and C.