Answer :
Let's solve the equation [tex]\(4|x+5| + 8 = 24\)[/tex] step by step.
1. Isolate the absolute value expression:
Start by subtracting 8 from both sides of the equation:
[tex]\[
4|x+5| = 24 - 8
\][/tex]
[tex]\[
4|x+5| = 16
\][/tex]
2. Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x+5| = \frac{16}{4}
\][/tex]
[tex]\[
|x+5| = 4
\][/tex]
3. Consider both possible cases for the absolute value equation:
- 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]
Therefore, the solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]. Thus, the correct choice is B. [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]\[
4|x+5| = 24 - 8
\][/tex]
[tex]\[
4|x+5| = 16
\][/tex]
2. Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x+5| = \frac{16}{4}
\][/tex]
[tex]\[
|x+5| = 4
\][/tex]
3. Consider both possible cases for the absolute value equation:
- 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]
Therefore, the solutions to the equation are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]. Thus, the correct choice is B. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].