High School

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 :

Let's solve the equation [tex]\(4|x+5| + 8 = 24\)[/tex] step by step.

1. Isolate the absolute value expression:

Start by subtracting 8 from both sides of the equation:
[tex]\[
4|x+5| = 24 - 8
\][/tex]
[tex]\[
4|x+5| = 16
\][/tex]

2. Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x+5| = \frac{16}{4}
\][/tex]
[tex]\[
|x+5| = 4
\][/tex]

3. Consider both possible cases for the absolute value equation:

- Case 1: [tex]\(x + 5 = 4\)[/tex]

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

- Case 2: [tex]\(x + 5 = -4\)[/tex]

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

Therefore, the solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]. Thus, the correct choice is B. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].