Algebra 1 Worksheet - Creating and Solving Equations - Free Printable

Problem: Solve the given equations step by step.

#### Equation 1: \( 12 + b = 42 \)

1. Subtract 12 from both sides:
\[
b = 42 - 12
\]
2. Simplify:
\[
b = 30
\]

Answer: \( b = 30 \)

---

#### Equation 2: \( m - 12 = -16 \)

1. Add 12 to both sides:
\[
m = -16 + 12
\]
2. Simplify:
\[
m = -4
\]

Answer: \( m = -4 \)

---

#### Equation 3: \( -224 = 4x \)

1. Divide both sides by 4:
\[
x = \frac{-224}{4}
\]
2. Simplify:
\[
x = -56
\]

Answer: \( x = -56 \)

---

#### Equation 4: \( -3 = \frac{b}{12} \)

1. Multiply both sides by 12:
\[
b = -3 \times 12
\]
2. Simplify:
\[
b = -36
\]

Answer: \( b = -36 \)

---

#### Equation 5: \( \frac{v}{4} = 12 \)

1. Multiply both sides by 4:
\[
v = 12 \times 4
\]
2. Simplify:
\[
v = 48
\]

Answer: \( v = 48 \)

---

#### Equation 6: \( 2(n + 3) = -12 \)

1. Distribute the 2 on the left-hand side:
\[
2n + 6 = -12
\]
2. Subtract 6 from both sides:
\[
2n = -12 - 6
\]
3. Simplify:
\[
2n = -18
\]
4. Divide both sides by 2:
\[
n = \frac{-18}{2}
\]
5. Simplify:
\[
n = -9
\]

Answer: \( n = -9 \)

---

#### Equation 7: \( -3 + \frac{x}{5} = -8 \)

1. Add 3 to both sides:
\[
\frac{x}{5} = -8 + 3
\]
2. Simplify:
\[
\frac{x}{5} = -5
\]
3. Multiply both sides by 5:
\[
x = -5 \times 5
\]
4. Simplify:
\[
x = -25
\]

Answer: \( x = -25 \)

---

#### Equation 8: \( -2 = \frac{x + 2}{6} \)

1. Multiply both sides by 6:
\[
-2 \times 6 = x + 2
\]
2. Simplify:
\[
-12 = x + 2
\]
3. Subtract 2 from both sides:
\[
x = -12 - 2
\]
4. Simplify:
\[
x = -14
\]

Answer: \( x = -14 \)

---

#### Equation 9: \( 2(n + 6) = -8 \)

1. Distribute the 2 on the left-hand side:
\[
2n + 12 = -8
\]
2. Subtract 12 from both sides:
\[
2n = -8 - 12
\]
3. Simplify:
\[
2n = -20
\]
4. Divide both sides by 2:
\[
n = \frac{-20}{2}
\]
5. Simplify:
\[
n = -10
\]

Answer: \( n = -10 \)

---

#### Equation 10: \( -3x - 20 = -155 \)

1. Add 20 to both sides:
\[
-3x = -155 + 20
\]
2. Simplify:
\[
-3x = -135
\]
3. Divide both sides by -3:
\[
x = \frac{-135}{-3}
\]
4. Simplify:
\[
x = 45
\]

Answer: \( x = 45 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \quad b = 30 \\
2. & \quad m = -4 \\
3. & \quad x = -56 \\
4. & \quad b = -36 \\
5. & \quad v = 48 \\
6. & \quad n = -9 \\
7. & \quad x = -25 \\
8. & \quad x = -14 \\
9. & \quad n = -10 \\
10. & \quad x = 45
\end{aligned}
}
\]