Answer :
To solve the equation [tex]\( |x + 5| - 6 = 7 \)[/tex], follow these steps:
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. Create two separate equations:
The expression inside the absolute value can be either positive or negative while still maintaining equality. Therefore, we split this into two separate equations:
[tex]\[
x + 5 = 13
\][/tex]
[tex]\[
x + 5 = -13
\][/tex]
3. Solve both equations:
- For the first equation [tex]\( x + 5 = 13 \)[/tex]:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For the second equation [tex]\( x + 5 = -13 \)[/tex]:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
4. Compile the solutions:
The solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are:
[tex]\[
x = 8 \text{ and } x = -18
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{B. \, x = 8 \text{ and } x = -18}
\][/tex]
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. Create two separate equations:
The expression inside the absolute value can be either positive or negative while still maintaining equality. Therefore, we split this into two separate equations:
[tex]\[
x + 5 = 13
\][/tex]
[tex]\[
x + 5 = -13
\][/tex]
3. Solve both equations:
- For the first equation [tex]\( x + 5 = 13 \)[/tex]:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For the second equation [tex]\( x + 5 = -13 \)[/tex]:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
4. Compile the solutions:
The solutions to the equation [tex]\( |x + 5| - 6 = 7 \)[/tex] are:
[tex]\[
x = 8 \text{ and } x = -18
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{B. \, x = 8 \text{ and } x = -18}
\][/tex]