High School

Given the function [tex]$f(x)=4|x-5|+3$[/tex], for what values of [tex]$x$[/tex] is [tex]$f(x)=15$[/tex]?

A. [tex]x=2, x=8[/tex]
B. [tex]x=1.5, x=8[/tex]
C. [tex]x=2, x=7.5[/tex]
D. [tex]x=0.5, x=7.5[/tex]

Answer :

Sure! Let's solve the problem step by step.

We are given the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex] and need to find the values of [tex]\( x \)[/tex] where [tex]\( f(x) = 15 \)[/tex].

1. Set the function equal to 15:

[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.

- First scenario: [tex]\( x - 5 = 3 \)[/tex]
[tex]\[
x = 3 + 5 = 8
\][/tex]

- Second scenario: [tex]\( x - 5 = -3 \)[/tex]
[tex]\[
x = -3 + 5 = 2
\][/tex]

Therefore, the values of [tex]\( x \)[/tex] that make [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex].

Thus, the correct answer is [tex]\( x=2, x=8 \)[/tex].

Other Questions