Question

solve $4|x + 5| + 8 = 24$
a. $x = 1$ and $x = -9$
b. $x = -1$ and $x = 9$
c. $x = -1$ and $x = -9$
d. $x = 1$ and $x = -1$

Explanation:

Step1: Isolate the absolute value term

Subtract 8 from both sides:
$4|x+5| + 8 - 8 = 24 - 8$
$4|x+5| = 16$

Step2: Simplify the equation

Divide both sides by 4:
$\frac{4|x+5|}{4} = \frac{16}{4}$
$|x+5| = 4$

Step3: Split into two cases

Case 1: $x+5 = 4$
Case 2: $x+5 = -4$

Step4: Solve Case 1

Subtract 5 from both sides:
$x = 4 - 5$
$x = -1$

Step5: Solve Case 2

Subtract 5 from both sides:
$x = -4 - 5$
$x = -9$

Answer:

C. $x = -1$ and $x = -9$