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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 steps to find these values:

1. Set the function equal to 15:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]

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

3. Divide by 4:
Divide both sides by 4 to further simplify:
[tex]\[
|x - 5| = 3
\][/tex]

4. Solve the absolute value equation:
The equation [tex]\( |x - 5| = 3 \)[/tex] gives us two possible equations to solve:
- [tex]\( x - 5 = 3 \)[/tex]
- [tex]\( x - 5 = -3 \)[/tex]

5. Solve each equation:
- For [tex]\( x - 5 = 3 \)[/tex]:
[tex]\[
x = 3 + 5 = 8
\][/tex]
- For [tex]\( x - 5 = -3 \)[/tex]:
[tex]\[
x = -3 + 5 = 2
\][/tex]

6. Conclude the solution:
The values of [tex]\(x\)[/tex] for which [tex]\(f(x) = 15\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = 8\)[/tex].

Therefore, the correct values of [tex]\(x\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = 8\)[/tex].

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Rewritten by : Jeany

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