Answer :
Sure! Let's solve the equation step-by-step.
The equation we need to solve is:
[tex]\[ 4|x+5| + 8 = 24 \][/tex]
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 to solve for the absolute value term:
[tex]\[
|x+5| = 4
\][/tex]
3. Set up two separate equations to handle the absolute value. Absolute values split into two scenarios:
- [tex]\( x+5 = 4 \)[/tex]
- [tex]\( x+5 = -4 \)[/tex]
4. Solve each equation separately:
- 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]
So, the solutions to the equation [tex]\( 4|x+5| + 8 = 24 \)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Therefore, the correct answer is:
D. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]
The equation we need to solve is:
[tex]\[ 4|x+5| + 8 = 24 \][/tex]
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 to solve for the absolute value term:
[tex]\[
|x+5| = 4
\][/tex]
3. Set up two separate equations to handle the absolute value. Absolute values split into two scenarios:
- [tex]\( x+5 = 4 \)[/tex]
- [tex]\( x+5 = -4 \)[/tex]
4. Solve each equation separately:
- 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]
So, the solutions to the equation [tex]\( 4|x+5| + 8 = 24 \)[/tex] are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Therefore, the correct answer is:
D. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]