Answer :
To solve the equation [tex]\(|x+5|-6=7\)[/tex], we'll follow these steps:
1. Isolate the Absolute Value:
Start by getting the absolute value expression by itself on one side of the equation:
[tex]\[
|x + 5| - 6 = 7
\][/tex]
Add 6 to both sides to isolate the absolute value:
[tex]\[
|x + 5| = 13
\][/tex]
2. Solve the Absolute Value Equation:
The equation [tex]\(|x + 5| = 13\)[/tex] means that the expression inside the absolute value can be either 13 or -13. We'll consider both cases:
- 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. Solutions:
The solutions to the equation [tex]\(|x+5| - 6 = 7\)[/tex] are [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
So, the correct answer is:
- [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
This matches option D.
1. Isolate the Absolute Value:
Start by getting the absolute value expression by itself on one side of the equation:
[tex]\[
|x + 5| - 6 = 7
\][/tex]
Add 6 to both sides to isolate the absolute value:
[tex]\[
|x + 5| = 13
\][/tex]
2. Solve the Absolute Value Equation:
The equation [tex]\(|x + 5| = 13\)[/tex] means that the expression inside the absolute value can be either 13 or -13. We'll consider both cases:
- 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. Solutions:
The solutions to the equation [tex]\(|x+5| - 6 = 7\)[/tex] are [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
So, the correct answer is:
- [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
This matches option D.