Solving Linear Equations worksheet featuring ten algebraic problems for practice.

To solve the given linear equations, we will isolate the variable on one side of the equation using basic algebraic operations. Let's solve each equation step by step.

---

Equation 1: \( 7x + 9 = 23 \)

1. Subtract 9 from both sides:
\[
7x + 9 - 9 = 23 - 9
\]
\[
7x = 14
\]
2. Divide both sides by 7:
\[
x = \frac{14}{7}
\]
\[
x = 2
\]

Solution: \( x = 2 \)

---

Equation 2: \( 4x + 17 = 18 \)

1. Subtract 17 from both sides:
\[
4x + 17 - 17 = 18 - 17
\]
\[
4x = 1
\]
2. Divide both sides by 4:
\[
x = \frac{1}{4}
\]

Solution: \( x = \frac{1}{4} \)

---

Equation 3: \( 9y + 5 = 41 \)

1. Subtract 5 from both sides:
\[
9y + 5 - 5 = 41 - 5
\]
\[
9y = 36
\]
2. Divide both sides by 9:
\[
y = \frac{36}{9}
\]
\[
y = 4
\]

Solution: \( y = 4 \)

---

Equation 4: \( 15x + 6 = 51 \)

1. Subtract 6 from both sides:
\[
15x + 6 - 6 = 51 - 6
\]
\[
15x = 45
\]
2. Divide both sides by 15:
\[
x = \frac{45}{15}
\]
\[
x = 3
\]

Solution: \( x = 3 \)

---

Equation 5: \( 12y + 9 = 69 \)

1. Subtract 9 from both sides:
\[
12y + 9 - 9 = 69 - 9
\]
\[
12y = 60
\]
2. Divide both sides by 12:
\[
y = \frac{60}{12}
\]
\[
y = 5
\]

Solution: \( y = 5 \)

---

Equation 6: \( 10y + 2 = 72 \)

1. Subtract 2 from both sides:
\[
10y + 2 - 2 = 72 - 2
\]
\[
10y = 70
\]
2. Divide both sides by 10:
\[
y = \frac{70}{10}
\]
\[
y = 7
\]

Solution: \( y = 7 \)

---

Equation 7: \( 6x + 8 = 32 \)

1. Subtract 8 from both sides:
\[
6x + 8 - 8 = 32 - 8
\]
\[
6x = 24
\]
2. Divide both sides by 6:
\[
x = \frac{24}{6}
\]
\[
x = 4
\]

Solution: \( x = 4 \)

---

Equation 8: \( 13x + 3 = 29 \)

1. Subtract 3 from both sides:
\[
13x + 3 - 3 = 29 - 3
\]
\[
13x = 26
\]
2. Divide both sides by 13:
\[
x = \frac{26}{13}
\]
\[
x = 2
\]

Solution: \( x = 2 \)

---

Equation 9: \( 4y + 7 = 19 \)

1. Subtract 7 from both sides:
\[
4y + 7 - 7 = 19 - 7
\]
\[
4y = 12
\]
2. Divide both sides by 4:
\[
y = \frac{12}{4}
\]
\[
y = 3
\]

Solution: \( y = 3 \)

---

Equation 10: \( 9y + 6 = 24 \)

1. Subtract 6 from both sides:
\[
9y + 6 - 6 = 24 - 6
\]
\[
9y = 18
\]
2. Divide both sides by 9:
\[
y = \frac{18}{9}
\]
\[
y = 2
\]

Solution: \( y = 2 \)

---

Equation 11: \( 8x + 8 = 48 \)

1. Subtract 8 from both sides:
\[
8x + 8 - 8 = 48 - 8
\]
\[
8x = 40
\]
2. Divide both sides by 8:
\[
x = \frac{40}{8}
\]
\[
x = 5
\]

Solution: \( x = 5 \)

---

Equation 12: \( 5x + 7 = 37 \)

1. Subtract 7 from both sides:
\[
5x + 7 - 7 = 37 - 7
\]
\[
5x = 30
\]
2. Divide both sides by 5:
\[
x = \frac{30}{5}
\]
\[
x = 6
\]

Solution: \( x = 6 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
&x = 2, \quad x = \frac{1}{4}, \quad y = 4, \quad x = 3, \quad y = 5, \quad y = 7, \\
&x = 4, \quad x = 2, \quad y = 3, \quad y = 2, \quad x = 5, \quad x = 6
\end{aligned}
}
\]