Printable worksheet featuring 12 algebra problems focused on applying the distributive property to solve for x.

The task involves solving equations using the distributive property. The distributive property states that:

\[
a(b + c) = ab + ac
\]

This means we can distribute the multiplication over addition or subtraction inside parentheses.

Let's solve each problem step by step.

---

Problem 1: \(3(1 - 2x) = 51\)

1. Distribute the 3:
\[
3(1) - 3(2x) = 51
\]
\[
3 - 6x = 51
\]

2. Isolate the term with \(x\):
\[
3 - 6x = 51
\]
Subtract 3 from both sides:
\[
-6x = 51 - 3
\]
\[
-6x = 48
\]

3. Solve for \(x\):
\[
x = \frac{48}{-6}
\]
\[
x = -8
\]

Answer: \(x = -8\)

---

Problem 2: \(4(3x + 6) = 16\)

1. Distribute the 4:
\[
4(3x) + 4(6) = 16
\]
\[
12x + 24 = 16
\]

2. Isolate the term with \(x\):
\[
12x + 24 = 16
\]
Subtract 24 from both sides:
\[
12x = 16 - 24
\]
\[
12x = -8
\]

3. Solve for \(x\):
\[
x = \frac{-8}{12}
\]
Simplify the fraction:
\[
x = -\frac{2}{3}
\]

Answer: \(x = -\frac{2}{3}\)

---

Problem 3: \(2(9 - 3x) = 90\)

1. Distribute the 2:
\[
2(9) - 2(3x) = 90
\]
\[
18 - 6x = 90
\]

2. Isolate the term with \(x\):
\[
18 - 6x = 90
\]
Subtract 18 from both sides:
\[
-6x = 90 - 18
\]
\[
-6x = 72
\]

3. Solve for \(x\):
\[
x = \frac{72}{-6}
\]
\[
x = -12
\]

Answer: \(x = -12\)

---

Problem 4: \(7(2x - 8) = -476\)

1. Distribute the 7:
\[
7(2x) - 7(8) = -476
\]
\[
14x - 56 = -476
\]

2. Isolate the term with \(x\):
\[
14x - 56 = -476
\]
Add 56 to both sides:
\[
14x = -476 + 56
\]
\[
14x = -420
\]

3. Solve for \(x\):
\[
x = \frac{-420}{14}
\]
\[
x = -30
\]

Answer: \(x = -30\)

---

Problem 5: \(3(2 - 4x) = 90\)

1. Distribute the 3:
\[
3(2) - 3(4x) = 90
\]
\[
6 - 12x = 90
\]

2. Isolate the term with \(x\):
\[
6 - 12x = 90
\]
Subtract 6 from both sides:
\[
-12x = 90 - 6
\]
\[
-12x = 84
\]

3. Solve for \(x\):
\[
x = \frac{84}{-12}
\]
\[
x = -7
\]

Answer: \(x = -7\)

---

Problem 6: \(2(3 + 3x) = 18\)

1. Distribute the 2:
\[
2(3) + 2(3x) = 18
\]
\[
6 + 6x = 18
\]

2. Isolate the term with \(x\):
\[
6 + 6x = 18
\]
Subtract 6 from both sides:
\[
6x = 18 - 6
\]
\[
6x = 12
\]

3. Solve for \(x\):
\[
x = \frac{12}{6}
\]
\[
x = 2
\]

Answer: \(x = 2\)

---

Problem 7: \(5(7 + 2x) = 155\)

1. Distribute the 5:
\[
5(7) + 5(2x) = 155
\]
\[
35 + 10x = 155
\]

2. Isolate the term with \(x\):
\[
35 + 10x = 155
\]
Subtract 35 from both sides:
\[
10x = 155 - 35
\]
\[
10x = 120
\]

3. Solve for \(x\):
\[
x = \frac{120}{10}
\]
\[
x = 12
\]

Answer: \(x = 12\)

---

Problem 8: \(-7(2 - 6x) = 196\)

1. Distribute the \(-7\):
\[
-7(2) - (-7)(6x) = 196
\]
\[
-14 + 42x = 196
\]

2. Isolate the term with \(x\):
\[
-14 + 42x = 196
\]
Add 14 to both sides:
\[
42x = 196 + 14
\]
\[
42x = 210
\]

3. Solve for \(x\):
\[
x = \frac{210}{42}
\]
\[
x = 5
\]

Answer: \(x = 5\)

---

Problem 9: \(7(3x + 7) = 280\)

1. Distribute the 7:
\[
7(3x) + 7(7) = 280
\]
\[
21x + 49 = 280
\]

2. Isolate the term with \(x\):
\[
21x + 49 = 280
\]
Subtract 49 from both sides:
\[
21x = 280 - 49
\]
\[
21x = 231
\]

3. Solve for \(x\):
\[
x = \frac{231}{21}
\]
\[
x = 11
\]

Answer: \(x = 11\)

---

Problem 10: \(5(9 - 6x) = 225\)

1. Distribute the 5:
\[
5(9) - 5(6x) = 225
\]
\[
45 - 30x = 225
\]

2. Isolate the term with \(x\):
\[
45 - 30x = 225
\]
Subtract 45 from both sides:
\[
-30x = 225 - 45
\]
\[
-30x = 180
\]

3. Solve for \(x\):
\[
x = \frac{180}{-30}
\]
\[
x = -6
\]

Answer: \(x = -6\)

---

Problem 11: \(-7(8 - 3x) = 273\)

1. Distribute the \(-7\):
\[
-7(8) - (-7)(3x) = 273
\]
\[
-56 + 21x = 273
\]

2. Isolate the term with \(x\):
\[
-56 + 21x = 273
\]
Add 56 to both sides:
\[
21x = 273 + 56
\]
\[
21x = 329
\]

3. Solve for \(x\):
\[
x = \frac{329}{21}
\]
Simplify the fraction:
\[
x = 15.6667 \quad \text{(or leave as a fraction if preferred)}
\]

Answer: \(x = \frac{329}{21}\) or approximately \(15.67\)

---

Problem 12: \(-6(8 + 4x) = -216\)

1. Distribute the \(-6\):
\[
-6(8) + (-6)(4x) = -216
\]
\[
-48 - 24x = -216
\]

2. Isolate the term with \(x\):
\[
-48 - 24x = -216
\]
Add 48 to both sides:
\[
-24x = -216 + 48
\]
\[
-24x = -168
\]

3. Solve for \(x\):
\[
x = \frac{-168}{-24}
\]
\[
x = 7
\]

Answer: \(x = 7\)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \quad x = -8 \\
2. & \quad x = -\frac{2}{3} \\
3. & \quad x = -12 \\
4. & \quad x = -30 \\
5. & \quad x = -7 \\
6. & \quad x = 2 \\
7. & \quad x = 12 \\
8. & \quad x = 5 \\
9. & \quad x = 11 \\
10. & \quad x = -6 \\
11. & \quad x = \frac{329}{21} \text{ or } 15.67 \\
12. & \quad x = 7 \\
\end{aligned}
}
\]