Answer :
Sure! Let's solve the equation step by step:
1. Start with the given equation:
[tex]\[
|x + 5| - 6 = 7
\][/tex]
2. Isolate the absolute value expression:
Add 6 to both sides of the equation to eliminate the -6:
[tex]\[
|x + 5| = 7 + 6
\][/tex]
[tex]\[
|x + 5| = 13
\][/tex]
3. Set up two separate equations:
The absolute value equation [tex]\(|x + 5| = 13\)[/tex] means that the expression [tex]\(x + 5\)[/tex] can be either 13 or -13. This gives us two cases to solve:
Case 1:
[tex]\[
x + 5 = 13
\][/tex]
Case 2:
[tex]\[
x + 5 = -13
\][/tex]
4. Solve each equation for [tex]\(x\)[/tex]:
- For Case 1:
Subtract 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For Case 2:
Subtract 5 from both sides:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
5. Write the 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:
- D. [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
1. Start with the given equation:
[tex]\[
|x + 5| - 6 = 7
\][/tex]
2. Isolate the absolute value expression:
Add 6 to both sides of the equation to eliminate the -6:
[tex]\[
|x + 5| = 7 + 6
\][/tex]
[tex]\[
|x + 5| = 13
\][/tex]
3. Set up two separate equations:
The absolute value equation [tex]\(|x + 5| = 13\)[/tex] means that the expression [tex]\(x + 5\)[/tex] can be either 13 or -13. This gives us two cases to solve:
Case 1:
[tex]\[
x + 5 = 13
\][/tex]
Case 2:
[tex]\[
x + 5 = -13
\][/tex]
4. Solve each equation for [tex]\(x\)[/tex]:
- For Case 1:
Subtract 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For Case 2:
Subtract 5 from both sides:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
5. Write the 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:
- D. [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].