Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Given the function [tex]$f(x) = 0.5|x-4| - 3$[/tex], for what values of [tex]$x$[/tex] is [tex]$f(x) = 7$[/tex]?

A. [tex]$x = -24, x = 16$[/tex]
B. [tex][tex]$x = -16, x = 24$[/tex][/tex]
C. [tex]$x = -1, x = 9$[/tex]
D. [tex]$x = 1, x = -9$[/tex]

Sagot :

GinnyAnswer
Let's solve the given equation [tex]\( f(x) = 7 \)[/tex] for the function [tex]\( f(x) = 0.5|x-4|-3 \)[/tex].

1. Start with the equation:
[tex]\[ f(x) = 7 \][/tex]
Substitute [tex]\( f(x) \)[/tex] with [tex]\( 0.5|x-4|-3 \)[/tex]:
[tex]\[ 0.5|x-4| - 3 = 7 \][/tex]

2. Add 3 to both sides of the equation to isolate the absolute value term:
[tex]\[ 0.5|x-4| = 10 \][/tex]

3. Multiply both sides by 2 to further isolate the absolute value term:
[tex]\[ |x-4| = 20 \][/tex]

4. The equation [tex]\( |x-4| = 20 \)[/tex] gives us two possible cases:
[tex]\[ x - 4 = 20 \quad \text{or} \quad x - 4 = -20 \][/tex]

5. Solve each case separately:
- Case 1: [tex]\( x - 4 = 20 \)[/tex]
[tex]\[ x = 20 + 4 \][/tex]
[tex]\[ x = 24 \][/tex]

- Case 2: [tex]\( x - 4 = -20 \)[/tex]
[tex]\[ x = -20 + 4 \][/tex]
[tex]\[ x = -16 \][/tex]

Thus, the solutions for the equation [tex]\( f(x) = 7 \)[/tex] are [tex]\( x = 24 \)[/tex] and [tex]\( x = -16 \)[/tex].

The correct answer is:
[tex]\[ x = -16, x = 24 \][/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.