Linear Equations - Worksheet Digital - Free Printable

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

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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: \( y = 4 \)

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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: \( x = 6 \)

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Final Answers:

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