Answer :
To solve the equation [tex]\( |x+5|-6=7 \)[/tex], follow these steps:
1. Isolate the Absolute Value:
Add 6 to both sides of the equation to get:
[tex]\[
|x+5| = 13
\][/tex]
2. Consider the Two Cases of the Absolute Value:
The expression inside the absolute value, [tex]\( x+5 \)[/tex], can equal either 13 or -13.
- Case 1: [tex]\( x+5 = 13 \)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = 13 - 5 = 8
\][/tex]
- Case 2: [tex]\( x+5 = -13 \)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = -13 - 5 = -18
\][/tex]
3. 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]\( D. \ x=8 \ \text{and} \ x=-18 \)[/tex].
1. Isolate the Absolute Value:
Add 6 to both sides of the equation to get:
[tex]\[
|x+5| = 13
\][/tex]
2. Consider the Two Cases of the Absolute Value:
The expression inside the absolute value, [tex]\( x+5 \)[/tex], can equal either 13 or -13.
- Case 1: [tex]\( x+5 = 13 \)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = 13 - 5 = 8
\][/tex]
- Case 2: [tex]\( x+5 = -13 \)[/tex]
- Subtract 5 from both sides:
[tex]\[
x = -13 - 5 = -18
\][/tex]
3. 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]\( D. \ x=8 \ \text{and} \ x=-18 \)[/tex].