Answer :
To solve the equation [tex]\( |x+5| - 6 = 7 \)[/tex], we will proceed step-by-step.
### Step-by-Step Solution
1. Isolate the Absolute Value Expression:
[tex]\[
|x+5| - 6 = 7
\][/tex]
Add 6 to both sides to isolate the absolute value:
[tex]\[
|x+5| = 13
\][/tex]
2. Consider the Definition of Absolute Value:
The absolute value equation [tex]\( |x+5| = 13 \)[/tex] means that [tex]\( x+5 \)[/tex] can be either 13 or -13. This gives us two separate equations:
[tex]\[
x + 5 = 13 \quad \text{or} \quad x + 5 = -13
\][/tex]
3. Solve Each Equation:
- For [tex]\( x + 5 = 13 \)[/tex]:
[tex]\[
x + 5 = 13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For [tex]\( x + 5 = -13 \)[/tex]:
[tex]\[
x + 5 = -13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
### Conclusion
The solutions to the equation [tex]\( |x+5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{\text{B. } x = 8 \text{ and } x = -18}
\][/tex]
### Step-by-Step Solution
1. Isolate the Absolute Value Expression:
[tex]\[
|x+5| - 6 = 7
\][/tex]
Add 6 to both sides to isolate the absolute value:
[tex]\[
|x+5| = 13
\][/tex]
2. Consider the Definition of Absolute Value:
The absolute value equation [tex]\( |x+5| = 13 \)[/tex] means that [tex]\( x+5 \)[/tex] can be either 13 or -13. This gives us two separate equations:
[tex]\[
x + 5 = 13 \quad \text{or} \quad x + 5 = -13
\][/tex]
3. Solve Each Equation:
- For [tex]\( x + 5 = 13 \)[/tex]:
[tex]\[
x + 5 = 13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For [tex]\( x + 5 = -13 \)[/tex]:
[tex]\[
x + 5 = -13
\][/tex]
Subtract 5 from both sides:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
### Conclusion
The solutions to the equation [tex]\( |x+5| - 6 = 7 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = -18 \)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{\text{B. } x = 8 \text{ and } x = -18}
\][/tex]