Answer :
Let's solve the equation [tex]\(4|x+5| + 8 = 24\)[/tex] step by step.
1. Simplify the equation:
We start by isolating the absolute value term:
[tex]\[
4|x+5| + 8 = 24
\][/tex]
Subtract 8 from both sides:
[tex]\[
4|x+5| = 16
\][/tex]
2. Divide by 4:
Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x+5| = 4
\][/tex]
3. Remove the absolute value:
The absolute value equation [tex]\(|x+5| = 4\)[/tex] gives us two possible equations:
[tex]\[
x+5 = 4 \quad \text{or} \quad x+5 = -4
\][/tex]
4. Solve each equation:
- For [tex]\(x+5 = 4\)[/tex]:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- For [tex]\(x+5 = -4\)[/tex]:
[tex]\[
x = -4 - 5 = -9
\][/tex]
5. Solution:
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:
A. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]
1. Simplify the equation:
We start by isolating the absolute value term:
[tex]\[
4|x+5| + 8 = 24
\][/tex]
Subtract 8 from both sides:
[tex]\[
4|x+5| = 16
\][/tex]
2. Divide by 4:
Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x+5| = 4
\][/tex]
3. Remove the absolute value:
The absolute value equation [tex]\(|x+5| = 4\)[/tex] gives us two possible equations:
[tex]\[
x+5 = 4 \quad \text{or} \quad x+5 = -4
\][/tex]
4. Solve each equation:
- For [tex]\(x+5 = 4\)[/tex]:
[tex]\[
x = 4 - 5 = -1
\][/tex]
- For [tex]\(x+5 = -4\)[/tex]:
[tex]\[
x = -4 - 5 = -9
\][/tex]
5. Solution:
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:
A. [tex]\(x = -1\)[/tex] and [tex]\(x = -9\)[/tex]