Question

1-Variable Equations & Inequalities Online Practice

Answer 1

It sounds like you're looking for practice on 1-variable equations and inequalities. Here are some examples, along with solutions to help you learn. You can try solving these on your own first, then check the solutions!

### Equations

1. **Solve for \( x \)**:
\[
2x + 3 = 11
\]

2. **Solve for \( x \)**:
\[
5 - 3x = 2
\]

3. **Solve for \( x \)**:
\[
4(x + 2) = 28
\]

4. **Solve for \( x \)**:
\[
\frac{x}{2} - 5 = 7
\]

5. **Solve for \( x \)**:
\[
3x + 4 = 2x - 6
\]

### Inequalities

1. **Solve the inequality**:
\[
3x - 1 < 5
\]

2. **Solve the inequality**:
\[
-2x + 4 \geq 10
\]

3. **Solve the inequality**:
\[
5 - x > 2x + 1
\]

4. **Solve the inequality**:
\[
4x + 7 \leq 3x + 15
\]

5. **Solve the inequality**:
\[
-3(x - 2) > 6
\]

### Solutions

**Equations:**

1. \( 2x + 3 = 11 \)
- Subtract 3: \( 2x = 8 \)
- Divide by 2: \( x = 4 \)

2. \( 5 - 3x = 2 \)
- Subtract 5: \( -3x = -3 \)
- Divide by -3: \( x = 1 \)

3. \( 4(x + 2) = 28 \)
- Divide by 4: \( x + 2 = 7 \)
- Subtract 2: \( x = 5 \)

4. \( \frac{x}{2} - 5 = 7 \)
- Add 5: \( \frac{x}{2} = 12 \)
- Multiply by 2: \( x = 24 \)

5. \( 3x + 4 = 2x - 6 \)
- Subtract \( 2x \): \( x + 4 = -6 \)
- Subtract 4: \( x = -10 \)

**Inequalities:**

1. \( 3x - 1 < 5 \)
- Add 1: \( 3x < 6 \)
- Divide by 3: \( x < 2 \)

2. \( -2x + 4 \geq 10 \)
- Subtract 4: \( -2x \geq 6 \)
- Divide by -2 (flip the inequality): \( x \leq -3 \)

3. \( 5 - x > 2x + 1 \)
- Add \( x \): \( 5 > 3x + 1 \)
- Subtract 1: \( 4 > 3x \)
- Divide by 3: \( \frac{4}{3} > x \) or \( x < \frac{4}{3} \)

4. \( 4x + 7 \leq 3x + 15 \)
- Subtract \( 3x \): \( x + 7 \leq 15 \)
- Subtract 7: \( x \leq 8 \)

5. \( -3(x - 2) > 6 \)
- Distribute: \( -3x + 6 > 6 \)
- Subtract 6: \( -3x > 0 \)
- Divide by -3 (flip the inequality): \( x < 0 \)

Feel free to reach out if you need more practice problems or further explanations!