Answer :
To solve the equation [tex]\(4|x+5| + 8 = 24\)[/tex], we need to isolate the absolute value expression. Let's go through the steps:
1. Subtract 8 from both sides:
[tex]\[
4|x+5| = 16
\][/tex]
2. Divide both sides by 4:
[tex]\[
|x+5| = 4
\][/tex]
3. Now, the absolute value equation [tex]\(|x+5| = 4\)[/tex] gives us two possible cases because the absolute value of a number is always positive:
- Case 1: [tex]\(x+5 = 4\)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- Case 2: [tex]\(x+5 = -4\)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = -4 - 5 = -9
\][/tex]
So, the solutions to the equation [tex]\(4|x+5| + 8 = 24\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Thus, the correct answer is:
A. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]
1. Subtract 8 from both sides:
[tex]\[
4|x+5| = 16
\][/tex]
2. Divide both sides by 4:
[tex]\[
|x+5| = 4
\][/tex]
3. Now, the absolute value equation [tex]\(|x+5| = 4\)[/tex] gives us two possible cases because the absolute value of a number is always positive:
- Case 1: [tex]\(x+5 = 4\)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- Case 2: [tex]\(x+5 = -4\)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = -4 - 5 = -9
\][/tex]
So, the solutions to the equation [tex]\(4|x+5| + 8 = 24\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex].
Thus, the correct answer is:
A. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]