Answer :
Let's solve the equation [tex]\(|x+5| - 6 = 7\)[/tex].
Step 1: Isolate the absolute value.
To start, we add 6 to both sides to isolate the absolute value expression:
[tex]\[
|x+5| = 13
\][/tex]
Step 2: Consider the definition of absolute value.
The expression [tex]\(|x+5| = 13\)[/tex] means that the expression inside the absolute value can either be 13 or -13. Therefore, we set up two separate equations:
1. [tex]\(x + 5 = 13\)[/tex]
2. [tex]\(x + 5 = -13\)[/tex]
Step 3: Solve each equation.
- For the equation [tex]\(x + 5 = 13\)[/tex]:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For the equation [tex]\(x + 5 = -13\)[/tex]:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
Step 4: Identify the solutions.
We have the solutions [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
Looking at the multiple-choice options, the correct answer is:
B. [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex]
Step 1: Isolate the absolute value.
To start, we add 6 to both sides to isolate the absolute value expression:
[tex]\[
|x+5| = 13
\][/tex]
Step 2: Consider the definition of absolute value.
The expression [tex]\(|x+5| = 13\)[/tex] means that the expression inside the absolute value can either be 13 or -13. Therefore, we set up two separate equations:
1. [tex]\(x + 5 = 13\)[/tex]
2. [tex]\(x + 5 = -13\)[/tex]
Step 3: Solve each equation.
- For the equation [tex]\(x + 5 = 13\)[/tex]:
[tex]\[
x = 13 - 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- For the equation [tex]\(x + 5 = -13\)[/tex]:
[tex]\[
x = -13 - 5
\][/tex]
[tex]\[
x = -18
\][/tex]
Step 4: Identify the solutions.
We have the solutions [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex].
Looking at the multiple-choice options, the correct answer is:
B. [tex]\(x = 8\)[/tex] and [tex]\(x = -18\)[/tex]