Answer :
To solve the equation [tex]\( |x-4| + 6 = 17 \)[/tex], we can first simplify it to isolate the absolute value:
1. Subtract 6 from both sides to get:
[tex]\[
|x-4| = 17 - 6
\][/tex]
2. Simplify the right side:
[tex]\[
|x-4| = 11
\][/tex]
Now that we have [tex]\( |x-4| = 11 \)[/tex], we can set up two cases to solve for [tex]\( x \)[/tex] because the absolute value expression [tex]\( |x-4| \)[/tex] means the value inside can be either 11 or -11:
Case 1: [tex]\( x-4 = 11 \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x - 4 = 11
\][/tex]
[tex]\[
x = 11 + 4
\][/tex]
[tex]\[
x = 15
\][/tex]
Case 2: [tex]\( x-4 = -11 \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x - 4 = -11
\][/tex]
[tex]\[
x = -11 + 4
\][/tex]
[tex]\[
x = -7
\][/tex]
So, the solutions are [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex].
Upon comparing these solutions with the given answer choices:
- The correct answer is B. [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex].
1. Subtract 6 from both sides to get:
[tex]\[
|x-4| = 17 - 6
\][/tex]
2. Simplify the right side:
[tex]\[
|x-4| = 11
\][/tex]
Now that we have [tex]\( |x-4| = 11 \)[/tex], we can set up two cases to solve for [tex]\( x \)[/tex] because the absolute value expression [tex]\( |x-4| \)[/tex] means the value inside can be either 11 or -11:
Case 1: [tex]\( x-4 = 11 \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x - 4 = 11
\][/tex]
[tex]\[
x = 11 + 4
\][/tex]
[tex]\[
x = 15
\][/tex]
Case 2: [tex]\( x-4 = -11 \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x - 4 = -11
\][/tex]
[tex]\[
x = -11 + 4
\][/tex]
[tex]\[
x = -7
\][/tex]
So, the solutions are [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex].
Upon comparing these solutions with the given answer choices:
- The correct answer is B. [tex]\( x = 15 \)[/tex] and [tex]\( x = -7 \)[/tex].
