Answer :
Sure! Let's solve the equation [tex]\(|x+5| - 6 = 7\)[/tex] step by step.
1. Start by isolating the absolute value expression:
[tex]\[
|x+5| - 6 = 7
\][/tex]
Add 6 to both sides to eliminate the -6:
[tex]\[
|x+5| = 13
\][/tex]
2. Now, we need to solve the equation considering the absolute value. This means we have two cases to consider:
- Case 1: [tex]\(x + 5 = 13\)[/tex]
- Case 2: [tex]\(x + 5 = -13\)[/tex]
3. Solve each case for [tex]\(x\)[/tex]:
- Case 1: [tex]\(x + 5 = 13\)[/tex]
Subtract 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- Case 2: [tex]\(x + 5 = -13\)[/tex]
Subtract 5 from both sides:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
4. Therefore, the solutions to the equation [tex]\(|x+5| - 6 = 7\)[/tex] are [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
The correct answer is option A: [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
1. Start by isolating the absolute value expression:
[tex]\[
|x+5| - 6 = 7
\][/tex]
Add 6 to both sides to eliminate the -6:
[tex]\[
|x+5| = 13
\][/tex]
2. Now, we need to solve the equation considering the absolute value. This means we have two cases to consider:
- Case 1: [tex]\(x + 5 = 13\)[/tex]
- Case 2: [tex]\(x + 5 = -13\)[/tex]
3. Solve each case for [tex]\(x\)[/tex]:
- Case 1: [tex]\(x + 5 = 13\)[/tex]
Subtract 5 from both sides:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- Case 2: [tex]\(x + 5 = -13\)[/tex]
Subtract 5 from both sides:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
4. Therefore, the solutions to the equation [tex]\(|x+5| - 6 = 7\)[/tex] are [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
The correct answer is option A: [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].