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 :

To solve for [tex]$x$[/tex] when
[tex]$$
f(x)=15,
$$[/tex]
given
[tex]$$
f(x)=4|x-5|+3,
$$[/tex]
follow these steps:

1. Write the equation:
[tex]$$
4|x-5|+3=15.
$$[/tex]

2. Subtract [tex]$3$[/tex] from both sides:
[tex]$$
4|x-5|=12.
$$[/tex]

3. Divide both sides by [tex]$4$[/tex]:
[tex]$$
|x-5|=3.
$$[/tex]

4. The absolute value equation [tex]$|x-5|=3$[/tex] has two cases:

- When [tex]$x-5=3$[/tex], solving gives:
[tex]$$
x=5+3=8.
$$[/tex]

- When [tex]$x-5=-3$[/tex], solving gives:
[tex]$$
x=5-3=2.
$$[/tex]

Thus, the solutions are [tex]$x = 2$[/tex] and [tex]$x = 8$[/tex].

Other Questions