Answer :
To solve the problem of finding the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] given the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex], follow these steps:
1. Set up the equation: Start by setting the given function equal to 15:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Isolate the absolute value: Subtract 3 from both sides to get:
[tex]\[
4|x-5| = 12
\][/tex]
3. Solve for the absolute value: Divide both sides by 4:
[tex]\[
|x-5| = 3
\][/tex]
4. Consider the two cases for the absolute value:
- Case 1: When [tex]\( x - 5 = 3 \)[/tex]
[tex]\[
x - 5 = 3
\][/tex]
Add 5 to both sides:
[tex]\[
x = 8
\][/tex]
- Case 2: When [tex]\( x - 5 = -3 \)[/tex]
[tex]\[
x - 5 = -3
\][/tex]
Add 5 to both sides:
[tex]\[
x = 2
\][/tex]
Therefore, the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
1. Set up the equation: Start by setting the given function equal to 15:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Isolate the absolute value: Subtract 3 from both sides to get:
[tex]\[
4|x-5| = 12
\][/tex]
3. Solve for the absolute value: Divide both sides by 4:
[tex]\[
|x-5| = 3
\][/tex]
4. Consider the two cases for the absolute value:
- Case 1: When [tex]\( x - 5 = 3 \)[/tex]
[tex]\[
x - 5 = 3
\][/tex]
Add 5 to both sides:
[tex]\[
x = 8
\][/tex]
- Case 2: When [tex]\( x - 5 = -3 \)[/tex]
[tex]\[
x - 5 = -3
\][/tex]
Add 5 to both sides:
[tex]\[
x = 2
\][/tex]
Therefore, the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
