College

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

A. [tex]$x=-1$[/tex] and [tex][tex]$x=9$[/tex][/tex]
B. [tex]$x=1$[/tex] and [tex]$x=-1$[/tex]
C. [tex][tex]$x=-1$[/tex][/tex] and [tex]$x=-9$[/tex]
D. [tex]$x=1$[/tex] and [tex][tex]$x=-9$[/tex][/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]
Divide both sides by 4:
[tex]\[
|x+5| = 4
\][/tex]

2. Solve for the variable inside the absolute value:
The equation [tex]\( |x+5| = 4 \)[/tex] gives us two cases to consider:
[tex]\[
x+5 = 4 \quad \text{or} \quad x+5 = -4
\][/tex]

- For the first case: [tex]\( x+5 = 4 \)[/tex]
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]

- For the second case: [tex]\( x+5 = -4 \)[/tex]
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]

3. Combine the solutions:
The solutions to the equation are:
[tex]\[
x = -1 \quad \text{and} \quad x = -9
\][/tex]

So, the correct answer is:
[tex]\[
\boxed{C. \, x=-1 \text{ and } x=-9}
\][/tex]