College

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

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

3. Set up the two possible equations:
- Absolute value equations have two scenarios to consider:
- [tex]\( x + 5 = 4 \)[/tex]
- [tex]\( x + 5 = -4 \)[/tex]

4. Solve each equation:

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

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

Therefore, the solutions to the equation [tex]\( 4|x+5| + 8 = 24 \)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]. The correct option is C: [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].