Question

question
use a graphing calculator to solve the following inequality.
$(x + 4)^2 - 2 > 23$

Explanation:

Step1: Isolate the squared term

Add 2 to both sides:
$$(x+4)^2 > 23 + 2$$
$$(x+4)^2 > 25$$

Step2: Take square roots

Recall $\sqrt{a^2}=|a|$, so:
$$|x+4| > 5$$

Step3: Split absolute value inequality

This splits into two cases:
Case 1: $x+4 > 5$
Case 2: $x+4 < -5$

Step4: Solve each case

Case1: Subtract 4 from both sides:
$x > 5 - 4$
$x > 1$

Case2: Subtract 4 from both sides:
$x < -5 - 4$
$x < -9$

Answer:

$x < -9$ or $x > 1$ (in interval notation: $(-\infty, -9) \cup (1, \infty)$)