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Solve [tex]$4|x+5|+8=24$[/tex].

A. [tex]x=1[/tex] and [tex]x=-9[/tex]
B. [tex]x=-1[/tex] and [tex]x=-9[/tex]
C. [tex]x=1[/tex] and [tex]x=-1[/tex]
D. [tex]x=-1[/tex] and [tex]x=9[/tex]

Answer :

To solve the equation [tex]\(4|x+5| + 8 = 24\)[/tex], follow these steps:

1. Isolate the Absolute Value Term:
- Start by subtracting 8 from both sides to get:
[tex]\[
4|x+5| = 16
\][/tex]

2. Simplify:
- Divide both sides by 4 to isolate the absolute value:
[tex]\[
|x+5| = 4
\][/tex]

3. Remove the Absolute Value:
- The equation [tex]\(|x+5| = 4\)[/tex] gives us two cases to consider:
- Case 1: [tex]\(x + 5 = 4\)[/tex]
- Case 2: [tex]\(x + 5 = -4\)[/tex]

4. Solve for [tex]\(x\)[/tex] in Each Case:

- Case 1:
[tex]\[
x + 5 = 4
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 4 - 5 = -1
\][/tex]

- Case 2:
[tex]\[
x + 5 = -4
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -4 - 5 = -9
\][/tex]

So the solutions to the equation [tex]\(4|x+5| + 8 = 24\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].

The correct answer is [tex]\( \boxed{B} \)[/tex] [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].

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