Answer :
We start with the equation:
[tex]$$4|x+5| = 24.$$[/tex]
Step 1: Isolate the absolute value by dividing both sides by 4:
[tex]$$
|x+5| = \frac{24}{4} = 6.
$$[/tex]
Step 2: Solve the absolute value equation. The equation [tex]$$|x+5|=6$$[/tex] leads to two cases:
1. When the expression inside the absolute value is positive:
[tex]$$
x+5 = 6 \quad \Longrightarrow \quad x = 6 - 5 = 1.
$$[/tex]
2. When the expression inside the absolute value is negative:
[tex]$$
x+5 = -6 \quad \Longrightarrow \quad x = -6 - 5 = -11.
$$[/tex]
Thus, the solutions are [tex]$$x = 1 \quad \text{and} \quad x = -11.$$[/tex]
Comparing with the answer choices, the correct option is:
B. [tex]\(x = -11\)[/tex] and [tex]\(x = 1\)[/tex].
[tex]$$4|x+5| = 24.$$[/tex]
Step 1: Isolate the absolute value by dividing both sides by 4:
[tex]$$
|x+5| = \frac{24}{4} = 6.
$$[/tex]
Step 2: Solve the absolute value equation. The equation [tex]$$|x+5|=6$$[/tex] leads to two cases:
1. When the expression inside the absolute value is positive:
[tex]$$
x+5 = 6 \quad \Longrightarrow \quad x = 6 - 5 = 1.
$$[/tex]
2. When the expression inside the absolute value is negative:
[tex]$$
x+5 = -6 \quad \Longrightarrow \quad x = -6 - 5 = -11.
$$[/tex]
Thus, the solutions are [tex]$$x = 1 \quad \text{and} \quad x = -11.$$[/tex]
Comparing with the answer choices, the correct option is:
B. [tex]\(x = -11\)[/tex] and [tex]\(x = 1\)[/tex].