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 :
To solve the problem where the function [tex]\( f(x) = 4|x - 5| + 3 \)[/tex] equals 15, follow these steps:
1. Set up the equation:
Start with the equation [tex]\( f(x) = 15 \)[/tex].
So, [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]\[ 4|x - 5| = 15 - 3 \][/tex]
[tex]\[ 4|x - 5| = 12 \][/tex]
3. Solve for the absolute value:
Divide both sides by 4 to further isolate the absolute value:
[tex]\[ |x - 5| = \frac{12}{4} \][/tex]
[tex]\[ |x - 5| = 3 \][/tex]
4. Consider both scenarios for the absolute value equation:
Since [tex]\( |x - 5| = 3 \)[/tex], this equation can be split into two separate linear equations:
- Case 1: [tex]\( x - 5 = 3 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 3 + 5 \][/tex]
[tex]\[ x = 8 \][/tex]
- Case 2: [tex]\( x - 5 = -3 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = -3 + 5 \][/tex]
[tex]\[ x = 2 \][/tex]
5. Conclusion:
The values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
Hence, the correct answer from the choices provided is [tex]\( x = 2, x = 8 \)[/tex].
1. Set up the equation:
Start with the equation [tex]\( f(x) = 15 \)[/tex].
So, [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]\[ 4|x - 5| = 15 - 3 \][/tex]
[tex]\[ 4|x - 5| = 12 \][/tex]
3. Solve for the absolute value:
Divide both sides by 4 to further isolate the absolute value:
[tex]\[ |x - 5| = \frac{12}{4} \][/tex]
[tex]\[ |x - 5| = 3 \][/tex]
4. Consider both scenarios for the absolute value equation:
Since [tex]\( |x - 5| = 3 \)[/tex], this equation can be split into two separate linear equations:
- Case 1: [tex]\( x - 5 = 3 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 3 + 5 \][/tex]
[tex]\[ x = 8 \][/tex]
- Case 2: [tex]\( x - 5 = -3 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[ x = -3 + 5 \][/tex]
[tex]\[ x = 2 \][/tex]
5. Conclusion:
The values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
Hence, the correct answer from the choices provided is [tex]\( x = 2, x = 8 \)[/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
