Solve 2-Step Equations worksheet featuring eight algebraic problems with fractions and variables.

To solve each of the given 2-step equations, we will follow a systematic approach. Let's solve them step by step.

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1. Solve \( \frac{3}{4}x + 6 = 15 \)

#### Step 1: Isolate the term with \( x \)
Subtract 6 from both sides:
\[
\frac{3}{4}x + 6 - 6 = 15 - 6
\]
\[
\frac{3}{4}x = 9
\]

#### Step 2: Solve for \( x \)
Multiply both sides by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \):
\[
x = 9 \cdot \frac{4}{3}
\]
\[
x = \frac{36}{3}
\]
\[
x = 12
\]

Solution: \( x = 12 \)

---

2. Solve \( \frac{2}{3}x - 4 = 1 \)

#### Step 1: Isolate the term with \( x \)
Add 4 to both sides:
\[
\frac{2}{3}x - 4 + 4 = 1 + 4
\]
\[
\frac{2}{3}x = 5
\]

#### Step 2: Solve for \( x \)
Multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):
\[
x = 5 \cdot \frac{3}{2}
\]
\[
x = \frac{15}{2}
\]
\[
x = 7.5
\]

Solution: \( x = 7.5 \)

---

3. Solve \( \frac{5}{6}x - 10 = 5 \)

#### Step 1: Isolate the term with \( x \)
Add 10 to both sides:
\[
\frac{5}{6}x - 10 + 10 = 5 + 10
\]
\[
\frac{5}{6}x = 15
\]

#### Step 2: Solve for \( x \)
Multiply both sides by the reciprocal of \( \frac{5}{6} \), which is \( \frac{6}{5} \):
\[
x = 15 \cdot \frac{6}{5}
\]
\[
x = \frac{90}{5}
\]
\[
x = 18
\]

Solution: \( x = 18 \)

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4. Solve \( 10 = \frac{2}{5}x - 8 \)

#### Step 1: Isolate the term with \( x \)
Add 8 to both sides:
\[
10 + 8 = \frac{2}{5}x - 8 + 8
\]
\[
18 = \frac{2}{5}x
\]

#### Step 2: Solve for \( x \)
Multiply both sides by the reciprocal of \( \frac{2}{5} \), which is \( \frac{5}{2} \):
\[
x = 18 \cdot \frac{5}{2}
\]
\[
x = \frac{90}{2}
\]
\[
x = 45
\]

Solution: \( x = 45 \)

---

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

#### Step 1: Isolate the term with \( x \)
Add 2 to both sides:
\[
\frac{4}{5}x - 2 + 2 = 2 + 2
\]
\[
\frac{4}{5}x = 4
\]

#### Step 2: Solve for \( x \)
Multiply both sides by the reciprocal of \( \frac{4}{5} \), which is \( \frac{5}{4} \):
\[
x = 4 \cdot \frac{5}{4}
\]
\[
x = \frac{20}{4}
\]
\[
x = 5
\]

Solution: \( x = 5 \)

---

6. Solve \( 6 = \frac{2}{3}x - 3 \)

#### Step 1: Isolate the term with \( x \)
Add 3 to both sides:
\[
6 + 3 = \frac{2}{3}x - 3 + 3
\]
\[
9 = \frac{2}{3}x
\]

#### Step 2: Solve for \( x \)
Multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \):
\[
x = 9 \cdot \frac{3}{2}
\]
\[
x = \frac{27}{2}
\]
\[
x = 13.5
\]

Solution: \( x = 13.5 \)

---

7. Solve \( 6 + \frac{7}{2}x = 13 \)

#### Step 1: Isolate the term with \( x \)
Subtract 6 from both sides:
\[
6 + \frac{7}{2}x - 6 = 13 - 6
\]
\[
\frac{7}{2}x = 7
\]

#### Step 2: Solve for \( x \)
Multiply both sides by the reciprocal of \( \frac{7}{2} \), which is \( \frac{2}{7} \):
\[
x = 7 \cdot \frac{2}{7}
\]
\[
x = \frac{14}{7}
\]
\[
x = 2
\]

Solution: \( x = 2 \)

---

8. Solve \( \frac{7}{8}x - 6 = 8 \)

#### Step 1: Isolate the term with \( x \)
Add 6 to both sides:
\[
\frac{7}{8}x - 6 + 6 = 8 + 6
\]
\[
\frac{7}{8}x = 14
\]

#### Step 2: Solve for \( x \)
Multiply both sides by the reciprocal of \( \frac{7}{8} \), which is \( \frac{8}{7} \):
\[
x = 14 \cdot \frac{8}{7}
\]
\[
x = \frac{112}{7}
\]
\[
x = 16
\]

Solution: \( x = 16 \)

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Final Answers:

\[
\boxed{12, 7.5, 18, 45, 5, 13.5, 2, 16}
\]