College

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 :

We start with the equation

[tex]$$
4|x-5| + 3 = 15.
$$[/tex]

Step 1: Subtract [tex]$3$[/tex] from both sides:

[tex]$$
4|x-5| = 12.
$$[/tex]

Step 2: Divide both sides by [tex]$4$[/tex]:

[tex]$$
|x-5| = 3.
$$[/tex]

Step 3: Solve the absolute value equation. The equation [tex]$|x-5| = 3$[/tex] means that the expression inside the absolute value can be either [tex]$3$[/tex] or [tex]$-3$[/tex]. That gives us two cases:

- Case 1:

[tex]$$
x - 5 = 3 \quad \Rightarrow \quad x = 8.
$$[/tex]

- Case 2:

[tex]$$
x - 5 = -3 \quad \Rightarrow \quad x = 2.
$$[/tex]

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

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