Algebraic equations - Free worksheets, PowerPoints and other - Free Printable

Problem: Solve for the variable in each equation.

The task involves solving 20 single-variable equations. Let's solve each equation step by step.

---

#### Equation 1: \( 5 - y = 2 \)
1. Subtract 5 from both sides:
\[
5 - y - 5 = 2 - 5
\]
\[
-y = -3
\]
2. Multiply both sides by -1 to solve for \( y \):
\[
y = 3
\]

Answer: \( y = 3 \)

---

#### Equation 2: \( 2 - y = -1 \)
1. Subtract 2 from both sides:
\[
2 - y - 2 = -1 - 2
\]
\[
-y = -3
\]
2. Multiply both sides by -1:
\[
y = 3
\]

Answer: \( y = 3 \)

---

#### Equation 3: \( 8 - y = 5 \)
1. Subtract 8 from both sides:
\[
8 - y - 8 = 5 - 8
\]
\[
-y = -3
\]
2. Multiply both sides by -1:
\[
y = 3
\]

Answer: \( y = 3 \)

---

#### Equation 4: \( y - 5 = 4 \)
1. Add 5 to both sides:
\[
y - 5 + 5 = 4 + 5
\]
\[
y = 9
\]

Answer: \( y = 9 \)

---

#### Equation 5: \( y + 4 = 7 \)
1. Subtract 4 from both sides:
\[
y + 4 - 4 = 7 - 4
\]
\[
y = 3
\]

Answer: \( y = 3 \)

---

#### Equation 6: \( y + 8 = 15 \)
1. Subtract 8 from both sides:
\[
y + 8 - 8 = 15 - 8
\]
\[
y = 7
\]

Answer: \( y = 7 \)

---

#### Equation 7: \( y + 4 = 13 \)
1. Subtract 4 from both sides:
\[
y + 4 - 4 = 13 - 4
\]
\[
y = 9
\]

Answer: \( y = 9 \)

---

#### Equation 8: \( y + 5 = 14 \)
1. Subtract 5 from both sides:
\[
y + 5 - 5 = 14 - 5
\]
\[
y = 9
\]

Answer: \( y = 9 \)

---

#### Equation 9: \( y - 3 = 6 \)
1. Add 3 to both sides:
\[
y - 3 + 3 = 6 + 3
\]
\[
y = 9
\]

Answer: \( y = 9 \)

---

#### Equation 10: \( y + 5 = 11 \)
1. Subtract 5 from both sides:
\[
y + 5 - 5 = 11 - 5
\]
\[
y = 6
\]

Answer: \( y = 6 \)

---

#### Equation 11: \( y + 7 = 13 \)
1. Subtract 7 from both sides:
\[
y + 7 - 7 = 13 - 7
\]
\[
y = 6
\]

Answer: \( y = 6 \)

---

#### Equation 12: \( y - 5 = 0 \)
1. Add 5 to both sides:
\[
y - 5 + 5 = 0 + 5
\]
\[
y = 5
\]

Answer: \( y = 5 \)

---

#### Equation 13: \( y + 6 = 13 \)
1. Subtract 6 from both sides:
\[
y + 6 - 6 = 13 - 6
\]
\[
y = 7
\]

Answer: \( y = 7 \)

---

#### Equation 14: \( y - 5 = -2 \)
1. Add 5 to both sides:
\[
y - 5 + 5 = -2 + 5
\]
\[
y = 3
\]

Answer: \( y = 3 \)

---

#### Equation 15: \( y - 8 = -4 \)
1. Add 8 to both sides:
\[
y - 8 + 8 = -4 + 8
\]
\[
y = 4
\]

Answer: \( y = 4 \)

---

#### Equation 16: \( y + 9 = 18 \)
1. Subtract 9 from both sides:
\[
y + 9 - 9 = 18 - 9
\]
\[
y = 9
\]

Answer: \( y = 9 \)

---

#### Equation 17: \( y + 3 = 12 \)
1. Subtract 3 from both sides:
\[
y + 3 - 3 = 12 - 3
\]
\[
y = 9
\]

Answer: \( y = 9 \)

---

#### Equation 18: \( 1 - y = -4 \)
1. Subtract 1 from both sides:
\[
1 - y - 1 = -4 - 1
\]
\[
-y = -5
\]
2. Multiply both sides by -1:
\[
y = 5
\]

Answer: \( y = 5 \)

---

#### Equation 19: \( y - 5 = 1 \)
1. Add 5 to both sides:
\[
y - 5 + 5 = 1 + 5
\]
\[
y = 6
\]

Answer: \( y = 6 \)

---

#### Equation 20: \( 6 - y = -2 \)
1. Subtract 6 from both sides:
\[
6 - y - 6 = -2 - 6
\]
\[
-y = -8
\]
2. Multiply both sides by -1:
\[
y = 8
\]

Answer: \( y = 8 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & y = 3 \\
2. & y = 3 \\
3. & y = 3 \\
4. & y = 9 \\
5. & y = 3 \\
6. & y = 7 \\
7. & y = 9 \\
8. & y = 9 \\
9. & y = 9 \\
10. & y = 6 \\
11. & y = 6 \\
12. & y = 5 \\
13. & y = 7 \\
14. & y = 3 \\
15. & y = 4 \\
16. & y = 9 \\
17. & y = 9 \\
18. & y = 5 \\
19. & y = 6 \\
20. & y = 8 \\
\end{array}
}
\]