Answer :
To solve the equation [tex]\(|x+5|-6=7\)[/tex], we need to follow these steps:
1. Isolate the absolute value expression:
Start by adding 6 to both sides of the equation to get:
[tex]\[
|x + 5| = 13
\][/tex]
2. Consider the two cases for the absolute value:
The absolute value equation [tex]\(|x + 5| = 13\)[/tex] means that the expression inside the absolute value, [tex]\(x + 5\)[/tex], can either be 13 or -13.
- Case 1: [tex]\(x + 5 = 13\)[/tex]
Solve for [tex]\(x\)[/tex] by subtracting 5 from both sides:
[tex]\[
x = 13 - 5 = 8
\][/tex]
- Case 2: [tex]\(x + 5 = -13\)[/tex]
Solve for [tex]\(x\)[/tex] by subtracting 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].
Therefore, the correct answer is Option D: [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
1. Isolate the absolute value expression:
Start by adding 6 to both sides of the equation to get:
[tex]\[
|x + 5| = 13
\][/tex]
2. Consider the two cases for the absolute value:
The absolute value equation [tex]\(|x + 5| = 13\)[/tex] means that the expression inside the absolute value, [tex]\(x + 5\)[/tex], can either be 13 or -13.
- Case 1: [tex]\(x + 5 = 13\)[/tex]
Solve for [tex]\(x\)[/tex] by subtracting 5 from both sides:
[tex]\[
x = 13 - 5 = 8
\][/tex]
- Case 2: [tex]\(x + 5 = -13\)[/tex]
Solve for [tex]\(x\)[/tex] by subtracting 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].
Therefore, the correct answer is Option D: [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].