Answer :
Let's solve the problem step-by-step:
We have the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex] and we want to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].
1. Set up the equation:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Solve for the absolute value:
First, subtract 3 from both sides to get:
[tex]\[
4|x-5| = 12
\][/tex]
3. Divide both sides by 4:
[tex]\[
|x-5| = 3
\][/tex]
4. Consider the two cases for the absolute value:
- Case 1: [tex]\( x-5 = 3 \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 3 + 5 = 8
\][/tex]
- Case 2: [tex]\( x-5 = -3 \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x = -3 + 5 = 2
\][/tex]
Thus, the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
So the correct answer is:
[tex]\( x=2, x=8 \)[/tex].
We have the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex] and we want to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].
1. Set up the equation:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Solve for the absolute value:
First, subtract 3 from both sides to get:
[tex]\[
4|x-5| = 12
\][/tex]
3. Divide both sides by 4:
[tex]\[
|x-5| = 3
\][/tex]
4. Consider the two cases for the absolute value:
- Case 1: [tex]\( x-5 = 3 \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 3 + 5 = 8
\][/tex]
- Case 2: [tex]\( x-5 = -3 \)[/tex]
- Solve for [tex]\( x \)[/tex]:
[tex]\[
x = -3 + 5 = 2
\][/tex]
Thus, the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
So the correct answer is:
[tex]\( x=2, x=8 \)[/tex].
