Solving One and Two-Step Equations - Lindsay Bowden - Free Printable

Problem: Solve each equation. Show all work.

#### Equation 1: $\frac{x}{5} - 2 = 9$
1. Add 2 to both sides:
\[
\frac{x}{5} - 2 + 2 = 9 + 2
\]
\[
\frac{x}{5} = 11
\]
2. Multiply both sides by 5:
\[
5 \cdot \frac{x}{5} = 11 \cdot 5
\]
\[
x = 55
\]

Solution: $x = 55$

---

#### Equation 2: $\frac{x}{3} = -20$
1. Multiply both sides by 3:
\[
3 \cdot \frac{x}{3} = -20 \cdot 3
\]
\[
x = -60
\]

Solution: $x = -60$

---

#### Equation 3: $-45 = 4x + 5x$
1. Combine like terms on the right side:
\[
-45 = 9x
\]
2. Divide both sides by 9:
\[
\frac{-45}{9} = \frac{9x}{9}
\]
\[
x = -5
\]

Solution: $x = -5$

---

#### Equation 4: $-8 - x = 11$
1. Add 8 to both sides:
\[
-8 - x + 8 = 11 + 8
\]
\[
-x = 19
\]
2. Multiply both sides by -1:
\[
x = -19
\]

Solution: $x = -19$

---

#### Equation 5: $\frac{x - 2}{6} = -4$
1. Multiply both sides by 6:
\[
6 \cdot \frac{x - 2}{6} = -4 \cdot 6
\]
\[
x - 2 = -24
\]
2. Add 2 to both sides:
\[
x - 2 + 2 = -24 + 2
\]
\[
x = -22
\]

Solution: $x = -22$

---

#### Equation 6: $5.5 + \frac{x}{2} = 8$
1. Subtract 5.5 from both sides:
\[
5.5 + \frac{x}{2} - 5.5 = 8 - 5.5
\]
\[
\frac{x}{2} = 2.5
\]
2. Multiply both sides by 2:
\[
2 \cdot \frac{x}{2} = 2.5 \cdot 2
\]
\[
x = 5
\]

Solution: $x = 5$

---

#### Equation 7: $\frac{x}{7} = 9$
1. Multiply both sides by 7:
\[
7 \cdot \frac{x}{7} = 9 \cdot 7
\]
\[
x = 63
\]

Solution: $x = 63$

---

#### Equation 8: $24 + 4x = 6x$
1. Subtract $4x$ from both sides:
\[
24 + 4x - 4x = 6x - 4x
\]
\[
24 = 2x
\]
2. Divide both sides by 2:
\[
\frac{24}{2} = \frac{2x}{2}
\]
\[
x = 12
\]

Solution: $x = 12$

---

#### Equation 9: $\frac{2}{5}x - 6 = 13$
1. Add 6 to both sides:
\[
\frac{2}{5}x - 6 + 6 = 13 + 6
\]
\[
\frac{2}{5}x = 19
\]
2. Multiply both sides by $\frac{5}{2}$:
\[
\frac{5}{2} \cdot \frac{2}{5}x = 19 \cdot \frac{5}{2}
\]
\[
x = \frac{95}{2}
\]
\[
x = 47.5
\]

Solution: $x = 47.5$

---

#### Equation 10: $x + 15 = 74$
1. Subtract 15 from both sides:
\[
x + 15 - 15 = 74 - 15
\]
\[
x = 59
\]

Solution: $x = 59$

---

#### Equation 11: $36 - x = 14$
1. Subtract 36 from both sides:
\[
36 - x - 36 = 14 - 36
\]
\[
-x = -22
\]
2. Multiply both sides by -1:
\[
x = 22
\]

Solution: $x = 22$

---

#### Equation 12: $\frac{x + 6}{2} = 12$
1. Multiply both sides by 2:
\[
2 \cdot \frac{x + 6}{2} = 12 \cdot 2
\]
\[
x + 6 = 24
\]
2. Subtract 6 from both sides:
\[
x + 6 - 6 = 24 - 6
\]
\[
x = 18
\]

Solution: $x = 18$

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & x = 55 \\
2. & x = -60 \\
3. & x = -5 \\
4. & x = -19 \\
5. & x = -22 \\
6. & x = 5 \\
7. & x = 63 \\
8. & x = 12 \\
9. & x = 47.5 \\
10. & x = 59 \\
11. & x = 22 \\
12. & x = 18 \\
\end{array}
}
\]