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Answer :
We begin with the function
[tex]$$
f(x) = 4|x-5| + 3.
$$[/tex]
We are asked to solve for [tex]$x$[/tex] when [tex]$f(x)=15$[/tex]. That is, we need to solve
[tex]$$
4|x-5| + 3 = 15.
$$[/tex]
Step 1. Subtract [tex]$3$[/tex] from both sides:
[tex]$$
4|x-5| = 15 - 3 = 12.
$$[/tex]
Step 2. Divide both sides by [tex]$4$[/tex] to isolate the absolute value:
[tex]$$
|x-5| = \frac{12}{4} = 3.
$$[/tex]
Step 3. Use the definition of absolute value. The equation [tex]$|x-5| = 3$[/tex] implies two cases:
- Case 1: [tex]$x - 5 = 3$[/tex], which gives
[tex]$$
x = 5 + 3 = 8.
$$[/tex]
- Case 2: [tex]$x - 5 = -3$[/tex], which gives
[tex]$$
x = 5 - 3 = 2.
$$[/tex]
Thus, the solutions are [tex]$x = 2$[/tex] and [tex]$x = 8$[/tex].
[tex]$$
f(x) = 4|x-5| + 3.
$$[/tex]
We are asked to solve for [tex]$x$[/tex] when [tex]$f(x)=15$[/tex]. That is, we need to solve
[tex]$$
4|x-5| + 3 = 15.
$$[/tex]
Step 1. Subtract [tex]$3$[/tex] from both sides:
[tex]$$
4|x-5| = 15 - 3 = 12.
$$[/tex]
Step 2. Divide both sides by [tex]$4$[/tex] to isolate the absolute value:
[tex]$$
|x-5| = \frac{12}{4} = 3.
$$[/tex]
Step 3. Use the definition of absolute value. The equation [tex]$|x-5| = 3$[/tex] implies two cases:
- Case 1: [tex]$x - 5 = 3$[/tex], which gives
[tex]$$
x = 5 + 3 = 8.
$$[/tex]
- Case 2: [tex]$x - 5 = -3$[/tex], which gives
[tex]$$
x = 5 - 3 = 2.
$$[/tex]
Thus, the solutions are [tex]$x = 2$[/tex] and [tex]$x = 8$[/tex].
Thank you for reading the article 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. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
