Algebra practice worksheet for solving linear equations, labeled as Worksheet 3.

Problem Overview:

The task is to solve for the variable \( y \) in each of the 20 given algebraic equations. We will solve each equation step by step.

---

Solutions:

#### Equations 1–10:
These are simple linear equations of the form \( ay = b \). To solve for \( y \), divide both sides by \( a \).

1. \( 12y = 108 \)
\[
y = \frac{108}{12} = 9
\]
Answer: \( y = 9 \)

2. \( 9y = 54 \)
\[
y = \frac{54}{9} = 6
\]
Answer: \( y = 6 \)

3. \( 11y = 99 \)
\[
y = \frac{99}{11} = 9
\]
Answer: \( y = 9 \)

4. \( 14y = 28 \)
\[
y = \frac{28}{14} = 2
\]
Answer: \( y = 2 \)

5. \( 9y = 45 \)
\[
y = \frac{45}{9} = 5
\]
Answer: \( y = 5 \)

6. \( 7y = 42 \)
\[
y = \frac{42}{7} = 6
\]
Answer: \( y = 6 \)

7. \( 10y = 80 \)
\[
y = \frac{80}{10} = 8
\]
Answer: \( y = 8 \)

8. \( 15y = 45 \)
\[
y = \frac{45}{15} = 3
\]
Answer: \( y = 3 \)

9. \( 6y = 48 \)
\[
y = \frac{48}{6} = 8
\]
Answer: \( y = 8 \)

10. \( 5y = 55 \)
\[
y = \frac{55}{5} = 11
\]
Answer: \( y = 11 \)

---

#### Equations 11–20:
These are more complex linear equations involving addition, subtraction, and multiplication. To solve for \( y \), isolate \( y \) on one side of the equation.

11. \( 6y + 15 = 45 \)
\[
6y = 45 - 15 \quad \text{(Subtract 15 from both sides)}
\]
\[
6y = 30
\]
\[
y = \frac{30}{6} = 5
\]
Answer: \( y = 5 \)

12. \( 9y + 15 = 60 \)
\[
9y = 60 - 15 \quad \text{(Subtract 15 from both sides)}
\]
\[
9y = 45
\]
\[
y = \frac{45}{9} = 5
\]
Answer: \( y = 5 \)

13. \( 4y + 13 = 33 \)
\[
4y = 33 - 13 \quad \text{(Subtract 13 from both sides)}
\]
\[
4y = 20
\]
\[
y = \frac{20}{4} = 5
\]
Answer: \( y = 5 \)

14. \( 7y + 8 = 50 \)
\[
7y = 50 - 8 \quad \text{(Subtract 8 from both sides)}
\]
\[
7y = 42
\]
\[
y = \frac{42}{7} = 6
\]
Answer: \( y = 6 \)

15. \( 5y + 19 = 79 \)
\[
5y = 79 - 19 \quad \text{(Subtract 19 from both sides)}
\]
\[
5y = 60
\]
\[
y = \frac{60}{5} = 12
\]
Answer: \( y = 12 \)

16. \( 12y - 12 = 48 \)
\[
12y = 48 + 12 \quad \text{(Add 12 to both sides)}
\]
\[
12y = 60
\]
\[
y = \frac{60}{12} = 5
\]
Answer: \( y = 5 \)

17. \( 8y - 13 = 27 \)
\[
8y = 27 + 13 \quad \text{(Add 13 to both sides)}
\]
\[
8y = 40
\]
\[
y = \frac{40}{8} = 5
\]
Answer: \( y = 5 \)

18. \( 5y - 10 = 15 \)
\[
5y = 15 + 10 \quad \text{(Add 10 to both sides)}
\]
\[
5y = 25
\]
\[
y = \frac{25}{5} = 5
\]
Answer: \( y = 5 \)

19. \( 3y - 13 = 20 \)
\[
3y = 20 + 13 \quad \text{(Add 13 to both sides)}
\]
\[
3y = 33
\]
\[
y = \frac{33}{3} = 11
\]
Answer: \( y = 11 \)

20. \( 6y - 12 = 60 \)
\[
6y = 60 + 12 \quad \text{(Add 12 to both sides)}
\]
\[
6y = 72
\]
\[
y = \frac{72}{6} = 12
\]
Answer: \( y = 12 \)

---

Final Answers:

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