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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 find the values of [tex]\( x \)[/tex] for which the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex] equals 15, we will go through the following steps:

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

2. Subtract 3 from both sides to simplify the equation:
[tex]\[
4|x - 5| = 12
\][/tex]

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

4. Solve the absolute value equation [tex]\( |x - 5| = 3 \)[/tex]. This equation means that the expression inside the absolute value, [tex]\( x - 5 \)[/tex], can be either 3 or -3. Therefore, we get two cases to consider:
[tex]\[
x - 5 = 3 \quad \text{or} \quad x - 5 = -3
\][/tex]

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

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

Thus, 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 is:
[tex]\[ x = 2, x = 8 \][/tex]

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Rewritten by : Jeany

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