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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 the problem, we need to find the values of [tex]\( x \)[/tex] for which the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex] equals 15. Let's go through the solution step by step:

1. Set up the equation:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]

2. Isolate the absolute value:
- Subtract 3 from both sides:
[tex]\[
4|x - 5| = 12
\][/tex]

3. Divide by 4:
- Divide both sides by 4 to solve for the absolute value:
[tex]\[
|x - 5| = 3
\][/tex]

4. Solve the absolute value equation:
- This equation implies two scenarios, because absolute value expressions can equal positive or negative of a number:
- Case 1:
[tex]\[
x - 5 = 3
\][/tex]
- Case 2:
[tex]\[
x - 5 = -3
\][/tex]

5. Solve each case:
- Case 1: Solve for [tex]\( x \)[/tex]
[tex]\[
x = 3 + 5 = 8
\][/tex]
- Case 2: Solve for [tex]\( x \)[/tex]
[tex]\[
x = -3 + 5 = 2
\][/tex]

The solutions for [tex]\( x \)[/tex] are 8 and 2. Therefore, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex]. The correct answer from the given options is [tex]\( x = 2, x = 8 \)[/tex].

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Rewritten by : Jeany

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