Simple Linear Equations (A) worksheet with 15 algebra problems to solve for variables.

Problem: Solve each of the given simple linear equations for the variable.

The worksheet contains 15 equations, and we will solve each one step by step. Here are the equations:

1. \( 8 - \frac{z}{2} = 5 \)
2. \( \frac{u}{4} + 5 = 7 \)
3. \( \frac{y}{7} + 8 = 13 \)
4. \( \frac{x}{4} + 5 = 9 \)
5. \( 1 + \frac{b}{8} = 8 \)
6. \( \frac{v}{3} + 3 = 7 \)
7. \( \frac{c}{5} - 3 = 3 \)
8. \( 2 + \frac{b}{3} = 7 \)
9. \( 2 + \frac{y}{9} = 11 \)
10. \( \frac{u}{5} + 10 = 17 \)
11. \( \frac{y}{2} + 8 = 15 \)
12. \( \frac{z}{7} + 10 = 12 \)
13. \( 8 + \frac{a}{5} = 12 \)
14. \( 6 + \frac{c}{9} = 12 \)
15. \( \frac{y}{2} + 8 = 12 \)

---

Solution:

#### Equation 1: \( 8 - \frac{z}{2} = 5 \)
1. Subtract 8 from both sides:
\[
-\frac{z}{2} = 5 - 8
\]
\[
-\frac{z}{2} = -3
\]
2. Multiply both sides by \(-2\):
\[
z = (-3) \times (-2)
\]
\[
z = 6
\]

Answer: \( z = 6 \)

---

#### Equation 2: \( \frac{u}{4} + 5 = 7 \)
1. Subtract 5 from both sides:
\[
\frac{u}{4} = 7 - 5
\]
\[
\frac{u}{4} = 2
\]
2. Multiply both sides by 4:
\[
u = 2 \times 4
\]
\[
u = 8
\]

Answer: \( u = 8 \)

---

#### Equation 3: \( \frac{y}{7} + 8 = 13 \)
1. Subtract 8 from both sides:
\[
\frac{y}{7} = 13 - 8
\]
\[
\frac{y}{7} = 5
\]
2. Multiply both sides by 7:
\[
y = 5 \times 7
\]
\[
y = 35
\]

Answer: \( y = 35 \)

---

#### Equation 4: \( \frac{x}{4} + 5 = 9 \)
1. Subtract 5 from both sides:
\[
\frac{x}{4} = 9 - 5
\]
\[
\frac{x}{4} = 4
\]
2. Multiply both sides by 4:
\[
x = 4 \times 4
\]
\[
x = 16
\]

Answer: \( x = 16 \)

---

#### Equation 5: \( 1 + \frac{b}{8} = 8 \)
1. Subtract 1 from both sides:
\[
\frac{b}{8} = 8 - 1
\]
\[
\frac{b}{8} = 7
\]
2. Multiply both sides by 8:
\[
b = 7 \times 8
\]
\[
b = 56
\]

Answer: \( b = 56 \)

---

#### Equation 6: \( \frac{v}{3} + 3 = 7 \)
1. Subtract 3 from both sides:
\[
\frac{v}{3} = 7 - 3
\]
\[
\frac{v}{3} = 4
\]
2. Multiply both sides by 3:
\[
v = 4 \times 3
\]
\[
v = 12
\]

Answer: \( v = 12 \)

---

#### Equation 7: \( \frac{c}{5} - 3 = 3 \)
1. Add 3 to both sides:
\[
\frac{c}{5} = 3 + 3
\]
\[
\frac{c}{5} = 6
\]
2. Multiply both sides by 5:
\[
c = 6 \times 5
\]
\[
c = 30
\]

Answer: \( c = 30 \)

---

#### Equation 8: \( 2 + \frac{b}{3} = 7 \)
1. Subtract 2 from both sides:
\[
\frac{b}{3} = 7 - 2
\]
\[
\frac{b}{3} = 5
\]
2. Multiply both sides by 3:
\[
b = 5 \times 3
\]
\[
b = 15
\]

Answer: \( b = 15 \)

---

#### Equation 9: \( 2 + \frac{y}{9} = 11 \)
1. Subtract 2 from both sides:
\[
\frac{y}{9} = 11 - 2
\]
\[
\frac{y}{9} = 9
\]
2. Multiply both sides by 9:
\[
y = 9 \times 9
\]
\[
y = 81
\]

Answer: \( y = 81 \)

---

#### Equation 10: \( \frac{u}{5} + 10 = 17 \)
1. Subtract 10 from both sides:
\[
\frac{u}{5} = 17 - 10
\]
\[
\frac{u}{5} = 7
\]
2. Multiply both sides by 5:
\[
u = 7 \times 5
\]
\[
u = 35
\]

Answer: \( u = 35 \)

---

#### Equation 11: \( \frac{y}{2} + 8 = 15 \)
1. Subtract 8 from both sides:
\[
\frac{y}{2} = 15 - 8
\]
\[
\frac{y}{2} = 7
\]
2. Multiply both sides by 2:
\[
y = 7 \times 2
\]
\[
y = 14
\]

Answer: \( y = 14 \)

---

#### Equation 12: \( \frac{z}{7} + 10 = 12 \)
1. Subtract 10 from both sides:
\[
\frac{z}{7} = 12 - 10
\]
\[
\frac{z}{7} = 2
\]
2. Multiply both sides by 7:
\[
z = 2 \times 7
\]
\[
z = 14
\]

Answer: \( z = 14 \)

---

#### Equation 13: \( 8 + \frac{a}{5} = 12 \)
1. Subtract 8 from both sides:
\[
\frac{a}{5} = 12 - 8
\]
\[
\frac{a}{5} = 4
\]
2. Multiply both sides by 5:
\[
a = 4 \times 5
\]
\[
a = 20
\]

Answer: \( a = 20 \)

---

#### Equation 14: \( 6 + \frac{c}{9} = 12 \)
1. Subtract 6 from both sides:
\[
\frac{c}{9} = 12 - 6
\]
\[
\frac{c}{9} = 6
\]
2. Multiply both sides by 9:
\[
c = 6 \times 9
\]
\[
c = 54
\]

Answer: \( c = 54 \)

---

#### Equation 15: \( \frac{y}{2} + 8 = 12 \)
1. Subtract 8 from both sides:
\[
\frac{y}{2} = 12 - 8
\]
\[
\frac{y}{2} = 4
\]
2. Multiply both sides by 2:
\[
y = 4 \times 2
\]
\[
y = 8
\]

Answer: \( y = 8 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \quad z = 6 \\
2. & \quad u = 8 \\
3. & \quad y = 35 \\
4. & \quad x = 16 \\
5. & \quad b = 56 \\
6. & \quad v = 12 \\
7. & \quad c = 30 \\
8. & \quad b = 15 \\
9. & \quad y = 81 \\
10. & \quad u = 35 \\
11. & \quad y = 14 \\
12. & \quad z = 14 \\
13. & \quad a = 20 \\
14. & \quad c = 54 \\
15. & \quad y = 8 \\
\end{aligned}
}
\]