College

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 :

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

1. Isolate the absolute value term:
[tex]\[
4|x+5| + 8 = 24
\][/tex]
Subtract 8 from both sides:
[tex]\[
4|x+5| = 16
\][/tex]

2. Divide both sides by 4:
[tex]\[
|x+5| = 4
\][/tex]

3. Solve the absolute value equation:
The equation [tex]\( |x+5| = 4 \)[/tex] means that [tex]\( x+5 \)[/tex] can be either 4 or -4.

So, let's consider the two cases:
- Case 1: [tex]\( x+5 = 4 \)[/tex]
- Case 2: [tex]\( x+5 = -4 \)[/tex]

4. Solve each case:

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

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

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

So, the correct answer is:

A. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]