High School

Solve [tex]4|x+7|+8=32[/tex].

A. [tex]x=1[/tex] and [tex]x=-13[/tex]
B. [tex]x=-1[/tex] and [tex]x=-13[/tex]
C. [tex]x=-1[/tex] and [tex]x=13[/tex]
D. [tex]x=1[/tex] and [tex]x=-1[/tex]

Answer :

To solve the equation [tex]\(4|x+7| + 8 = 32\)[/tex], we should follow these steps:

1. Isolate the Absolute Value Expression:
Begin by subtracting 8 from both sides of the equation:
[tex]\[
4|x + 7| = 32 - 8
\][/tex]
[tex]\[
4|x + 7| = 24
\][/tex]

2. Divide by 4 to Simplify:
Divide both sides of the equation by 4:
[tex]\[
|x + 7| = \frac{24}{4}
\][/tex]
[tex]\[
|x + 7| = 6
\][/tex]

3. Set Up Two Separate Equations:
The absolute value equation [tex]\( |x + 7| = 6 \)[/tex] can be rewritten as two separate equations:
[tex]\[
x + 7 = 6 \quad \text{and} \quad x + 7 = -6
\][/tex]

4. Solve Each Equation:
- For the equation [tex]\( x + 7 = 6 \)[/tex]:
Subtract 7 from both sides:
[tex]\[
x = 6 - 7
\][/tex]
[tex]\[
x = -1
\][/tex]

- For the equation [tex]\( x + 7 = -6 \)[/tex]:
Subtract 7 from both sides:
[tex]\[
x = -6 - 7
\][/tex]
[tex]\[
x = -13
\][/tex]

5. Conclusion:
The solutions to the original equation [tex]\(4|x+7|+8=32\)[/tex] are [tex]\(x = -1\)[/tex] and [tex]\(x = -13\)[/tex].

Therefore, the correct answer is B. [tex]\( x = -1 \)[/tex] and [tex]\( x = -13 \)[/tex].