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]\[
4|x + 5| + 8 - 8 = 24 - 8
\][/tex]
[tex]\[
4|x + 5| = 16
\][/tex]
2. Divide both sides by 4:
[tex]\[
\frac{4|x + 5|}{4} = \frac{16}{4}
\][/tex]
[tex]\[
|x + 5| = 4
\][/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]
- Subtract 5 from both sides:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
- Case 2: [tex]\( x + 5 = -4 \)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
4. Write the solutions:
The solutions to the equation are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Thus, the correct answer is:
- [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]
So, the correct option is D. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
1. Isolate the absolute value expression:
Start by subtracting 8 from both sides of the equation:
[tex]\[
4|x + 5| + 8 - 8 = 24 - 8
\][/tex]
[tex]\[
4|x + 5| = 16
\][/tex]
2. Divide both sides by 4:
[tex]\[
\frac{4|x + 5|}{4} = \frac{16}{4}
\][/tex]
[tex]\[
|x + 5| = 4
\][/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]
- Subtract 5 from both sides:
[tex]\[
x = 4 - 5
\][/tex]
[tex]\[
x = -1
\][/tex]
- Case 2: [tex]\( x + 5 = -4 \)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = -4 - 5
\][/tex]
[tex]\[
x = -9
\][/tex]
4. Write the solutions:
The solutions to the equation are [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].
Thus, the correct answer is:
- [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex]
So, the correct option is D. [tex]\( x = -1 \)[/tex] and [tex]\( x = -9 \)[/tex].