Question

question
solve the following inequality algebraically.
$|x - 4| < 8$

Explanation:

Step1: Apply absolute value inequality rule

For $|A| < B$ (where $B>0$), this translates to $-B < A < B$. So:
$-8 < x - 4 < 8$

Step2: Add 4 to all three parts

Isolate $x$ by adding 4 to each segment of the inequality:
$-8 + 4 < x - 4 + 4 < 8 + 4$

Step3: Simplify all expressions

Calculate each term to find the range of $x$:
$-4 < x < 12$

Answer:

$-4 < x < 12$