Linear Equations - Worksheet Digital - Free Printable

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.

---

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: \( x = 2 \)

---

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

---

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: \( y = 4 \)

---

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: \( x = 3 \)

---

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: \( y = 5 \)

---

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: \( y = 7 \)

---

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: \( x = 4 \)

---

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: \( x = 2 \)

---

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: \( y = 3 \)

---

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: \( y = 2 \)

---

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: \( x = 5 \)

---

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:

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