Thank you for visiting 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. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
We are given the function
[tex]$$
f(x)=4|x-5|+3
$$[/tex]
and we need to find the values of [tex]$x$[/tex] for which
[tex]$$
f(x)=15.
$$[/tex]
Step 1. Set up the equation:
[tex]$$
4|x-5|+3=15.
$$[/tex]
Step 2. Subtract [tex]$3$[/tex] from both sides to isolate the term with the absolute value:
[tex]$$
4|x-5|=15-3=12.
$$[/tex]
Step 3. Divide both sides by [tex]$4$[/tex]:
[tex]$$
|x-5|=\frac{12}{4}=3.
$$[/tex]
Step 4. The equation [tex]$|x-5|=3$[/tex] means that the expression inside the absolute value, [tex]$x-5$[/tex], can be either [tex]$3$[/tex] or [tex]$-3$[/tex]. So, we have two cases:
1) [tex]$$x-5=3 \quad \Rightarrow \quad x=3+5=8,$$[/tex]
2) [tex]$$x-5=-3 \quad \Rightarrow \quad x=-3+5=2.$$[/tex]
Thus, the two solutions are [tex]$x=2$[/tex] and [tex]$x=8$[/tex].
Final Answer: The values of [tex]$x$[/tex] that satisfy [tex]$f(x)=15$[/tex] are [tex]$$x=2 \quad \text{and} \quad x=8.$$[/tex]
[tex]$$
f(x)=4|x-5|+3
$$[/tex]
and we need to find the values of [tex]$x$[/tex] for which
[tex]$$
f(x)=15.
$$[/tex]
Step 1. Set up the equation:
[tex]$$
4|x-5|+3=15.
$$[/tex]
Step 2. Subtract [tex]$3$[/tex] from both sides to isolate the term with the absolute value:
[tex]$$
4|x-5|=15-3=12.
$$[/tex]
Step 3. Divide both sides by [tex]$4$[/tex]:
[tex]$$
|x-5|=\frac{12}{4}=3.
$$[/tex]
Step 4. The equation [tex]$|x-5|=3$[/tex] means that the expression inside the absolute value, [tex]$x-5$[/tex], can be either [tex]$3$[/tex] or [tex]$-3$[/tex]. So, we have two cases:
1) [tex]$$x-5=3 \quad \Rightarrow \quad x=3+5=8,$$[/tex]
2) [tex]$$x-5=-3 \quad \Rightarrow \quad x=-3+5=2.$$[/tex]
Thus, the two solutions are [tex]$x=2$[/tex] and [tex]$x=8$[/tex].
Final Answer: The values of [tex]$x$[/tex] that satisfy [tex]$f(x)=15$[/tex] are [tex]$$x=2 \quad \text{and} \quad x=8.$$[/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!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
