Solve: |4x – 8| < 5 Give your answer as an interval. Check Answer

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## Solving Absolute Value Inequalities

### Problem Statement

Solve the following inequality and provide your answer as an interval:

\[ |4x - 8| < 5 \]

### Solution Steps

1. **Understanding the Inequality:**
   The expression \(|4x - 8| < 5\) implies that the absolute value of \(4x - 8\) is less than 5. This can be split into two separate inequalities:

   \[
   -5 < 4x - 8 < 5
   \]

2. **Solving the Inequalities:**
   - Separate the compound inequality into two parts:
     
     \[
     4x - 8 > -5 \quad \text{and} \quad 4x - 8 < 5
     \]

   - Solve each part individually:
     - For \(4x - 8 > -5\):
       \[
       4x - 8 > -5 \\
       4x > -5 + 8 \\
       4x > 3 \\
       x > \frac{3}{4} \\
       x > 0.75
       \]

     - For \(4x - 8 < 5\):
       \[
       4x - 8 < 5 \\
       4x < 5 + 8 \\
       4x < 13 \\
       x < \frac{13}{4} \\
       x < 3.25
       \]

3. **Combining the Solutions:**
   - The solutions \(x > 0.75\) and \(x < 3.25\) combine to form the interval:
   
     \[
     0.75 < x < 3.25
     \]

4. **Writing the Answer as an Interval:**
   - Express the solution in interval notation:
   
     \[
     (0.75, 3.25)
     \]

### Final Step

Enter the interval \((0.75, 3.25)\) in the answer box and click the "Check Answer" button.

### Interactive Elements
- **Input Box:**
  - Placeholder text: "Enter interval here"
  - Input type: Text
- **Button:**
  - Label: "Check Answer"

This interactive problem helps in understanding how to
Transcribed Image Text:## Solving Absolute Value Inequalities ### Problem Statement Solve the following inequality and provide your answer as an interval: \[ |4x - 8| < 5 \] ### Solution Steps 1. **Understanding the Inequality:** The expression \(|4x - 8| < 5\) implies that the absolute value of \(4x - 8\) is less than 5. This can be split into two separate inequalities: \[ -5 < 4x - 8 < 5 \] 2. **Solving the Inequalities:** - Separate the compound inequality into two parts: \[ 4x - 8 > -5 \quad \text{and} \quad 4x - 8 < 5 \] - Solve each part individually: - For \(4x - 8 > -5\): \[ 4x - 8 > -5 \\ 4x > -5 + 8 \\ 4x > 3 \\ x > \frac{3}{4} \\ x > 0.75 \] - For \(4x - 8 < 5\): \[ 4x - 8 < 5 \\ 4x < 5 + 8 \\ 4x < 13 \\ x < \frac{13}{4} \\ x < 3.25 \] 3. **Combining the Solutions:** - The solutions \(x > 0.75\) and \(x < 3.25\) combine to form the interval: \[ 0.75 < x < 3.25 \] 4. **Writing the Answer as an Interval:** - Express the solution in interval notation: \[ (0.75, 3.25) \] ### Final Step Enter the interval \((0.75, 3.25)\) in the answer box and click the "Check Answer" button. ### Interactive Elements - **Input Box:** - Placeholder text: "Enter interval here" - Input type: Text - **Button:** - Label: "Check Answer" This interactive problem helps in understanding how to
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