Question

question
solve the following inequality algebraically.
$|x - 4| \geq 12$
answer attempt 1 out of 2

Explanation:

Step1: Apply absolute value rule

For $|A| \geq B$, this splits to $A \geq B$ or $A \leq -B$.
So $x-4 \geq 12$ or $x-4 \leq -12$.

Step2: Solve first inequality

Add 4 to both sides.
$x-4 + 4 \geq 12 + 4$
$x \geq 16$

Step3: Solve second inequality

Add 4 to both sides.
$x-4 + 4 \leq -12 + 4$
$x \leq -8$

Answer:

$x \leq -8$ or $x \geq 16$