This pre-algebra worksheet provides 10 practice problems where students solve for the variable y using inverse operations and show their work.

Problem Overview:

The task involves solving a series of pre-algebra equations for the variable \( y \). Each equation contains terms involving \( y \) and constants, and we need to isolate \( y \) using inverse operations. Let's solve each equation step by step.

---

Equation 1: \( y + 8 + 7y = 56 \)

1. Combine like terms:
\[
y + 7y + 8 = 56
\]
\[
8y + 8 = 56
\]

2. Subtract 8 from both sides:
\[
8y + 8 - 8 = 56 - 8
\]
\[
8y = 48
\]

3. Divide both sides by 8:
\[
\frac{8y}{8} = \frac{48}{8}
\]
\[
y = 6
\]

Solution: \( y = 6 \)

---

Equation 2: \( y + 4 + 5 \times y = 64 \)

1. Simplify the multiplication:
\[
y + 4 + 5y = 64
\]

2. Combine like terms:
\[
y + 5y + 4 = 64
\]
\[
6y + 4 = 64
\]

3. Subtract 4 from both sides:
\[
6y + 4 - 4 = 64 - 4
\]
\[
6y = 60
\]

4. Divide both sides by 6:
\[
\frac{6y}{6} = \frac{60}{6}
\]
\[
y = 10
\]

Solution: \( y = 10 \)

---

Equation 3: \( y + 10 + 6 \times y = 80 \)

1. Simplify the multiplication:
\[
y + 10 + 6y = 80
\]

2. Combine like terms:
\[
y + 6y + 10 = 80
\]
\[
7y + 10 = 80
\]

3. Subtract 10 from both sides:
\[
7y + 10 - 10 = 80 - 10
\]
\[
7y = 70
\]

4. Divide both sides by 7:
\[
\frac{7y}{7} = \frac{70}{7}
\]
\[
y = 10
\]

Solution: \( y = 10 \)

---

Equation 4: \( y + 2 + 6 \times y = 86 \)

1. Simplify the multiplication:
\[
y + 2 + 6y = 86
\]

2. Combine like terms:
\[
y + 6y + 2 = 86
\]
\[
7y + 2 = 86
\]

3. Subtract 2 from both sides:
\[
7y + 2 - 2 = 86 - 2
\]
\[
7y = 84
\]

4. Divide both sides by 7:
\[
\frac{7y}{7} = \frac{84}{7}
\]
\[
y = 12
\]

Solution: \( y = 12 \)

---

Equation 5: \( y + 3 + 12 \times y = 42 \)

1. Simplify the multiplication:
\[
y + 3 + 12y = 42
\]

2. Combine like terms:
\[
y + 12y + 3 = 42
\]
\[
13y + 3 = 42
\]

3. Subtract 3 from both sides:
\[
13y + 3 - 3 = 42 - 3
\]
\[
13y = 39
\]

4. Divide both sides by 13:
\[
\frac{13y}{13} = \frac{39}{13}
\]
\[
y = 3
\]

Solution: \( y = 3 \)

---

Equation 6: \( y + 12 + 9 \times y = 52 \)

1. Simplify the multiplication:
\[
y + 12 + 9y = 52
\]

2. Combine like terms:
\[
y + 9y + 12 = 52
\]
\[
10y + 12 = 52
\]

3. Subtract 12 from both sides:
\[
10y + 12 - 12 = 52 - 12
\]
\[
10y = 40
\]

4. Divide both sides by 10:
\[
\frac{10y}{10} = \frac{40}{10}
\]
\[
y = 4
\]

Solution: \( y = 4 \)

---

Equation 7: \( y + 1 + 4 \times y = 11 \)

1. Simplify the multiplication:
\[
y + 1 + 4y = 11
\]

2. Combine like terms:
\[
y + 4y + 1 = 11
\]
\[
5y + 1 = 11
\]

3. Subtract 1 from both sides:
\[
5y + 1 - 1 = 11 - 1
\]
\[
5y = 10
\]

4. Divide both sides by 5:
\[
\frac{5y}{5} = \frac{10}{5}
\]
\[
y = 2
\]

Solution: \( y = 2 \)

---

Equation 8: \( y + 8 + 7 \times y = 88 \)

1. Simplify the multiplication:
\[
y + 8 + 7y = 88
\]

2. Combine like terms:
\[
y + 7y + 8 = 88
\]
\[
8y + 8 = 88
\]

3. Subtract 8 from both sides:
\[
8y + 8 - 8 = 88 - 8
\]
\[
8y = 80
\]

4. Divide both sides by 8:
\[
\frac{8y}{8} = \frac{80}{8}
\]
\[
y = 10
\]

Solution: \( y = 10 \)

---

Equation 9: \( y + 6 + 10 \times y = 50 \)

1. Simplify the multiplication:
\[
y + 6 + 10y = 50
\]

2. Combine like terms:
\[
y + 10y + 6 = 50
\]
\[
11y + 6 = 50
\]

3. Subtract 6 from both sides:
\[
11y + 6 - 6 = 50 - 6
\]
\[
11y = 44
\]

4. Divide both sides by 11:
\[
\frac{11y}{11} = \frac{44}{11}
\]
\[
y = 4
\]

Solution: \( y = 4 \)

---

Equation 10: \( y + 5 + 9 \times y = 125 \)

1. Simplify the multiplication:
\[
y + 5 + 9y = 125
\]

2. Combine like terms:
\[
y + 9y + 5 = 125
\]
\[
10y + 5 = 125
\]

3. Subtract 5 from both sides:
\[
10y + 5 - 5 = 125 - 5
\]
\[
10y = 120
\]

4. Divide both sides by 10:
\[
\frac{10y}{10} = \frac{120}{10}
\]
\[
y = 12
\]

Solution: \( y = 12 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ y = 6 \\
2. & \ y = 10 \\
3. & \ y = 10 \\
4. & \ y = 12 \\
5. & \ y = 3 \\
6. & \ y = 4 \\
7. & \ y = 2 \\
8. & \ y = 10 \\
9. & \ y = 4 \\
10. & \ y = 12 \\
\end{aligned}
}
\]