To solve the equation [tex]\( |x+6| - 7 = 8 \)[/tex]:
1. Isolate the absolute value term:
[tex]\[
|x+6| - 7 = 8
\][/tex]
Add 7 to both sides to isolate the absolute value expression:
[tex]\[
|x+6| = 8 + 7
\][/tex]
[tex]\[
|x+6| = 15
\][/tex]
2. Set up two separate equations:
The expression [tex]\( |x+6| = 15 \)[/tex] means that [tex]\( x+6 \)[/tex] could be equal to 15 or -15.
[tex]\[
x + 6 = 15 \quad \text{or} \quad x + 6 = -15
\][/tex]
3. Solve each equation separately:
[tex]\[
x + 6 = 15 \quad \Rightarrow \quad x = 15 - 6 \quad \Rightarrow \quad x = 9
\][/tex]
[tex]\[
x + 6 = -15 \quad \Rightarrow \quad x = -15 - 6 \quad \Rightarrow \quad x = -21
\][/tex]
4. Write the solutions:
The solutions to the equation [tex]\( |x+6| - 7 = 8 \)[/tex] are:
[tex]\[
x = 9 \quad \text{and} \quad x = -21
\][/tex]
Therefore, the correct answer is [tex]\( \boxed{B \ x=9 \ \text{and} \ x=-21} \)[/tex].
