High School

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

A. [tex]x = 1[/tex] and [tex]x = -1[/tex]
B. [tex]x = -1[/tex] and [tex]x = -9[/tex]
C. [tex]x = 1[/tex] and [tex]x = -9[/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:
[tex]\[
4|x+5| + 8 = 24
\][/tex]
Subtract 8 from both sides:
[tex]\[
4|x+5| = 16
\][/tex]

2. Solve for the absolute value:
Divide both sides by 4:
[tex]\[
|x+5| = 4
\][/tex]

3. Split into two separate equations:
Since the absolute value of [tex]\(x+5\)[/tex] equals 4, [tex]\(x+5\)[/tex] could be 4 or [tex]\(-4\)[/tex]:
[tex]\[
x + 5 = 4 \quad \text{or} \quad x + 5 = -4
\][/tex]

4. Solve each equation:
- For [tex]\(x + 5 = 4\)[/tex]:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
- For [tex]\(x + 5 = -4\)[/tex]:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]

5. Conclusion:
The solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]. Therefore, the correct answer is:

[tex]\[
\boxed{B. \, x=-1 \text{ and } x=-9}
\][/tex]