Answer :
To solve the equation [tex]\(4|x+5| + 8 = 24\)[/tex], let's go through the steps:
1. Subtract 8 from both sides to isolate the absolute value expression:
[tex]\[
4|x+5| = 16
\][/tex]
2. Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x+5| = 4
\][/tex]
3. The absolute value equation [tex]\( |x+5| = 4 \)[/tex] gives us two separate equations to solve:
- First equation: [tex]\( x+5 = 4 \)[/tex]
- Second equation: [tex]\( x+5 = -4 \)[/tex]
4. Solve the first equation [tex]\( x+5 = 4 \)[/tex]:
- Subtract 5 from both sides:
[tex]\[
x = 4 - 5
\][/tex]
- This gives us:
[tex]\[
x = -1
\][/tex]
5. Solve the second equation [tex]\( x+5 = -4 \)[/tex]:
- Subtract 5 from both sides:
[tex]\[
x = -4 - 5
\][/tex]
- This gives us:
[tex]\[
x = -9
\][/tex]
Therefore, the solutions to the equation are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
The correct option is:
D. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]
1. Subtract 8 from both sides to isolate the absolute value expression:
[tex]\[
4|x+5| = 16
\][/tex]
2. Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x+5| = 4
\][/tex]
3. The absolute value equation [tex]\( |x+5| = 4 \)[/tex] gives us two separate equations to solve:
- First equation: [tex]\( x+5 = 4 \)[/tex]
- Second equation: [tex]\( x+5 = -4 \)[/tex]
4. Solve the first equation [tex]\( x+5 = 4 \)[/tex]:
- Subtract 5 from both sides:
[tex]\[
x = 4 - 5
\][/tex]
- This gives us:
[tex]\[
x = -1
\][/tex]
5. Solve the second equation [tex]\( x+5 = -4 \)[/tex]:
- Subtract 5 from both sides:
[tex]\[
x = -4 - 5
\][/tex]
- This gives us:
[tex]\[
x = -9
\][/tex]
Therefore, the solutions to the equation are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
The correct option is:
D. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]