Linear Equation Worksheets (printable, online, answers, examples) - Free Printable

To solve each of the given linear equations, we will follow a systematic approach. Let's solve them step by step.

---

1. Solve \( \frac{6x + 5}{5} = 7 \)

#### Step 1: Eliminate the denominator
Multiply both sides of the equation by 5:
\[
5 \cdot \frac{6x + 5}{5} = 5 \cdot 7
\]
\[
6x + 5 = 35
\]

#### Step 2: Isolate the term with \( x \)
Subtract 5 from both sides:
\[
6x + 5 - 5 = 35 - 5
\]
\[
6x = 30
\]

#### Step 3: Solve for \( x \)
Divide both sides by 6:
\[
x = \frac{30}{6}
\]
\[
x = 5
\]

#### Final Answer:
\[
\boxed{x = 5}
\]

---

2. Solve \( 9 = \frac{4x - 5}{3} \)

#### Step 1: Eliminate the denominator
Multiply both sides of the equation by 3:
\[
3 \cdot 9 = 3 \cdot \frac{4x - 5}{3}
\]
\[
27 = 4x - 5
\]

#### Step 2: Isolate the term with \( x \)
Add 5 to both sides:
\[
27 + 5 = 4x - 5 + 5
\]
\[
32 = 4x
\]

#### Step 3: Solve for \( x \)
Divide both sides by 4:
\[
x = \frac{32}{4}
\]
\[
x = 8
\]

#### Final Answer:
\[
\boxed{x = 8}
\]

---

3. Solve \( \frac{5x - 5}{5} = 6 \)

#### Step 1: Eliminate the denominator
Multiply both sides of the equation by 5:
\[
5 \cdot \frac{5x - 5}{5} = 5 \cdot 6
\]
\[
5x - 5 = 30
\]

#### Step 2: Isolate the term with \( x \)
Add 5 to both sides:
\[
5x - 5 + 5 = 30 + 5
\]
\[
5x = 35
\]

#### Step 3: Solve for \( x \)
Divide both sides by 5:
\[
x = \frac{35}{5}
\]
\[
x = 7
\]

#### Final Answer:
\[
\boxed{x = 7}
\]

---

4. Solve \( \frac{7x - 5}{5} = 6 \)

#### Step 1: Eliminate the denominator
Multiply both sides of the equation by 5:
\[
5 \cdot \frac{7x - 5}{5} = 5 \cdot 6
\]
\[
7x - 5 = 30
\]

#### Step 2: Isolate the term with \( x \)
Add 5 to both sides:
\[
7x - 5 + 5 = 30 + 5
\]
\[
7x = 35
\]

#### Step 3: Solve for \( x \)
Divide both sides by 7:
\[
x = \frac{35}{7}
\]
\[
x = 5
\]

#### Final Answer:
\[
\boxed{x = 5}
\]

---

5. Solve \( 5 = \frac{6x + 2}{4} \)

#### Step 1: Eliminate the denominator
Multiply both sides of the equation by 4:
\[
4 \cdot 5 = 4 \cdot \frac{6x + 2}{4}
\]
\[
20 = 6x + 2
\]

#### Step 2: Isolate the term with \( x \)
Subtract 2 from both sides:
\[
20 - 2 = 6x + 2 - 2
\]
\[
18 = 6x
\]

#### Step 3: Solve for \( x \)
Divide both sides by 6:
\[
x = \frac{18}{6}
\]
\[
x = 3
\]

#### Final Answer:
\[
\boxed{x = 3}
\]

---

6. Solve \( \frac{4x + 8}{4} = 6 \)

#### Step 1: Eliminate the denominator
Multiply both sides of the equation by 4:
\[
4 \cdot \frac{4x + 8}{4} = 4 \cdot 6
\]
\[
4x + 8 = 24
\]

#### Step 2: Isolate the term with \( x \)
Subtract 8 from both sides:
\[
4x + 8 - 8 = 24 - 8
\]
\[
4x = 16
\]

#### Step 3: Solve for \( x \)
Divide both sides by 4:
\[
x = \frac{16}{4}
\]
\[
x = 4
\]

#### Final Answer:
\[
\boxed{x = 4}
\]

---

7. Solve \( \frac{6x + 9}{3} = 13 \)

#### Step 1: Eliminate the denominator
Multiply both sides of the equation by 3:
\[
3 \cdot \frac{6x + 9}{3} = 3 \cdot 13
\]
\[
6x + 9 = 39
\]

#### Step 2: Isolate the term with \( x \)
Subtract 9 from both sides:
\[
6x + 9 - 9 = 39 - 9
\]
\[
6x = 30
\]

#### Step 3: Solve for \( x \)
Divide both sides by 6:
\[
x = \frac{30}{6}
\]
\[
x = 5
\]

#### Final Answer:
\[
\boxed{x = 5}
\]

---

8. Solve \( 2 = \frac{3x - 2}{5} \)

#### Step 1: Eliminate the denominator
Multiply both sides of the equation by 5:
\[
5 \cdot 2 = 5 \cdot \frac{3x - 2}{5}
\]
\[
10 = 3x - 2
\]

#### Step 2: Isolate the term with \( x \)
Add 2 to both sides:
\[
10 + 2 = 3x - 2 + 2
\]
\[
12 = 3x
\]

#### Step 3: Solve for \( x \)
Divide both sides by 3:
\[
x = \frac{12}{3}
\]
\[
x = 4
\]

#### Final Answer:
\[
\boxed{x = 4}
\]

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Final Answers:

1. \( \boxed{x = 5} \)
2. \( \boxed{x = 8} \)
3. \( \boxed{x = 7} \)
4. \( \boxed{x = 5} \)
5. \( \boxed{x = 3} \)
6. \( \boxed{x = 4} \)
7. \( \boxed{x = 5} \)
8. \( \boxed{x = 4} \)