Question

absolute value inequalities (level 1)
score: 0/1 penalty: 1 off
question
solve the following inequality algebraically.
|x + 8| < 8
answer

Explanation:

Step1: Rewrite absolute value inequality

For $|A| < b$ where $b>0$, this is equivalent to $-b < A < b$. So:
$-8 < x + 8 < 8$

Step2: Subtract 8 from all parts

Subtract 8 to isolate $x$:
$-8 - 8 < x + 8 - 8 < 8 - 8$

Step3: Simplify all expressions

Calculate each segment of the inequality:
$-16 < x < 0$

Answer:

$-16 < x < 0$