Question

solve $4|x + 5| = 24$. \
\
\\(\bigcirc\\) a. \\(x = 11\\) and \\(x = -11\\) \
\\(\bigcirc\\) b. \\(x = -11\\) and \\(x = 1\\) \
\\(\bigcirc\\) c. \\(x = 11\\) and \\(x = -1\\) \
\\(\bigcirc\\) d. \\(x = -11\\) and \\(x = -1\\)

Explanation:

Step1: Isolate the absolute value

Divide both sides by 4:
$$\frac{4|x+5|}{4} = \frac{24}{4}$$
Simplify to get:
$$|x+5| = 6$$

Step2: Split into two cases

Case 1: Inside absolute value is non-negative:
$$x+5 = 6$$
Case 2: Inside absolute value is negative:
$$x+5 = -6$$

Step3: Solve Case 1

Subtract 5 from both sides:
$$x = 6 - 5$$
$$x = 1$$

Step4: Solve Case 2

Subtract 5 from both sides:
$$x = -6 - 5$$
$$x = -11$$

Answer:

B. $x=-11$ and $x=1$