Solve the absolute value inequality 2|x−8|−1<5 . Provide the answer using interval notation.(1 point)

Question

The solution to 2|x−8|−1<5
is (

Answer 1

To solve the inequality \( 2|x - 8| - 1 < 5 \), we will follow the steps outlined below:

1. Isolate the absolute value: \[ 2|x - 8| - 1 < 5 \] Add 1 to both sides: \[ 2|x - 8| < 6 \] Divide both sides by 2: \[ |x - 8| < 3 \]

2. Remove the absolute value by writing two inequalities: \[ -3 < x - 8 < 3 \]

3. Solve the inequalities: For the left part: \[ -3 < x - 8 \quad \Rightarrow \quad x > 5 \] For the right part: \[ x - 8 < 3 \quad \Rightarrow \quad x < 11 \]

4. Combine the results: \[ 5 < x < 11 \]

5. Write the solution in interval notation: The solution in interval notation is: \[ (5, 11) \]

So, the solution to the inequality \( 2|x - 8| - 1 < 5 \) is \((5, 11)\).