Question

use a graphing calculator to solve the following inequality. 4|x + 10|+6≥18

Explanation:

Step1: Isolate the absolute - value term

Subtract 6 from both sides of the inequality:
$4|x + 10|+6-6\geq18 - 6$
$4|x + 10|\geq12$

Step2: Further isolate the absolute - value

Divide both sides by 4:
$\frac{4|x + 10|}{4}\geq\frac{12}{4}$
$|x + 10|\geq3$

Step3: Solve the compound inequality

Case 1: $x+10\geq3$
Subtract 10 from both sides: $x+10 - 10\geq3 - 10$
$x\geq - 7$
Case 2: $x + 10\leq - 3$
Subtract 10 from both sides: $x+10 - 10\leq - 3-10$
$x\leq - 13$

Answer:

$x\leq - 13$ or $x\geq - 7$