Answer :
Let's solve the equation step-by-step:
We are given the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex]. We need to find the values of [tex]\( x \)[/tex] that make [tex]\( f(x) = 15 \)[/tex].
1. Set up the equation:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]
2. Subtract 3 from both sides:
[tex]\[
4|x - 5| = 12
\][/tex]
3. Divide both sides by 4:
[tex]\[
|x - 5| = 3
\][/tex]
4. Solve the absolute value equation:
The equation [tex]\( |x - 5| = 3 \)[/tex] means that [tex]\( x - 5 \)[/tex] can be 3 or -3.
- 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]
5. Solution:
The solutions are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
Therefore, the correct answer is [tex]\( x = 2, x = 8 \)[/tex].
We are given the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex]. We need to find the values of [tex]\( x \)[/tex] that make [tex]\( f(x) = 15 \)[/tex].
1. Set up the equation:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]
2. Subtract 3 from both sides:
[tex]\[
4|x - 5| = 12
\][/tex]
3. Divide both sides by 4:
[tex]\[
|x - 5| = 3
\][/tex]
4. Solve the absolute value equation:
The equation [tex]\( |x - 5| = 3 \)[/tex] means that [tex]\( x - 5 \)[/tex] can be 3 or -3.
- 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]
5. Solution:
The solutions are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
Therefore, the correct answer is [tex]\( x = 2, x = 8 \)[/tex].
