(8) Solve the inequality: \( |2 w-5|+4>13 \)

To solve the inequality \( |2w - 5| + 4 > 13 \), follow these steps: 1. **Isolate the Absolute Value:** \[ |2w - 5| + 4 > 13 \] Subtract 4 from both sides: \[ |2w - 5| > 9 \] 2. **Break Down the Absolute Value Inequality:** The inequality \( |A| > B \) (where \( B > 0 \)) can be rewritten as two separate inequalities: \[ A > B \quad \text{or} \quad A < -B \] Applying this to our problem: \[ 2w - 5 > 9 \quad \text{or} \quad 2w - 5 < -9 \] 3. **Solve Each Inequality Separately:** - **First Inequality:** \[ 2w - 5 > 9 \] Add 5 to both sides: \[ 2w > 14 \] Divide by 2: \[ w > 7 \] - **Second Inequality:** \[ 2w - 5 < -9 \] Add 5 to both sides: \[ 2w < -4 \] Divide by 2: \[ w < -2 \] 4. **Combine the Solutions:** The solution to the inequality is: \[ w < -2 \quad \text{or} \quad w > 7 \] **Final Answer:** All real numbers w with w < –2 or w greater than seven. In other words, w < −2 or w > 7