Answer :
To solve the equation [tex]\(4|x+5| + 8 = 24\)[/tex], let's break it down step-by-step:
1. Subtract 8 from both sides:
[tex]\[
4|x+5| + 8 - 8 = 24 - 8 \\
4|x+5| = 16
\][/tex]
2. Divide both sides by 4:
[tex]\[
\frac{4|x+5|}{4} = \frac{16}{4} \\
|x+5| = 4
\][/tex]
3. Solve the absolute value equation:
The equation [tex]\( |x+5| = 4 \)[/tex] can be split into two separate equations:
- Case 1: [tex]\( x+5 = 4 \)[/tex]
[tex]\[
x = 4 - 5 \\
x = -1
\][/tex]
- Case 2: [tex]\( x+5 = -4 \)[/tex]
[tex]\[
x = -4 - 5 \\
x = -9
\][/tex]
Therefore, the solutions are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Thus, the correct answer is D. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
1. Subtract 8 from both sides:
[tex]\[
4|x+5| + 8 - 8 = 24 - 8 \\
4|x+5| = 16
\][/tex]
2. Divide both sides by 4:
[tex]\[
\frac{4|x+5|}{4} = \frac{16}{4} \\
|x+5| = 4
\][/tex]
3. Solve the absolute value equation:
The equation [tex]\( |x+5| = 4 \)[/tex] can be split into two separate equations:
- Case 1: [tex]\( x+5 = 4 \)[/tex]
[tex]\[
x = 4 - 5 \\
x = -1
\][/tex]
- Case 2: [tex]\( x+5 = -4 \)[/tex]
[tex]\[
x = -4 - 5 \\
x = -9
\][/tex]
Therefore, the solutions are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Thus, the correct answer is D. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].