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 start with the equation
[tex]$$
4|x-5| + 3 = 15.
$$[/tex]
Step 1: Isolate the absolute term
Subtract 3 from both sides to get:
[tex]$$
4|x-5| = 15 - 3 = 12.
$$[/tex]
Step 2: Solve for the absolute value
Divide both sides by 4:
[tex]$$
|x-5| = \frac{12}{4} = 3.
$$[/tex]
Step 3: Solve the absolute value equation
The equation [tex]$|x-5| = 3$[/tex] has two cases:
1. Case 1: When the expression inside the absolute value is positive:
[tex]$$
x-5 = 3 \quad \Longrightarrow \quad x = 5 + 3 = 8.
$$[/tex]
2. Case 2: When the expression inside the absolute value is negative:
[tex]$$
x-5 = -3 \quad \Longrightarrow \quad x = 5 - 3 = 2.
$$[/tex]
Thus, the solutions are [tex]$x = 2$[/tex] and [tex]$x = 8$[/tex].
Final Answer: [tex]$x = 2 \text{ or } x = 8$[/tex].
[tex]$$
4|x-5| + 3 = 15.
$$[/tex]
Step 1: Isolate the absolute term
Subtract 3 from both sides to get:
[tex]$$
4|x-5| = 15 - 3 = 12.
$$[/tex]
Step 2: Solve for the absolute value
Divide both sides by 4:
[tex]$$
|x-5| = \frac{12}{4} = 3.
$$[/tex]
Step 3: Solve the absolute value equation
The equation [tex]$|x-5| = 3$[/tex] has two cases:
1. Case 1: When the expression inside the absolute value is positive:
[tex]$$
x-5 = 3 \quad \Longrightarrow \quad x = 5 + 3 = 8.
$$[/tex]
2. Case 2: When the expression inside the absolute value is negative:
[tex]$$
x-5 = -3 \quad \Longrightarrow \quad x = 5 - 3 = 2.
$$[/tex]
Thus, the solutions are [tex]$x = 2$[/tex] and [tex]$x = 8$[/tex].
Final Answer: [tex]$x = 2 \text{ or } x = 8$[/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
