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Answer :
To find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] given the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex], we need to solve the equation [tex]\( 4|x-5| + 3 = 15 \)[/tex].
Here's a step-by-step solution:
1. Start with the given equation:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Isolate the absolute value term:
[tex]\[
4|x-5| + 3 - 3 = 15 - 3
\][/tex]
[tex]\[
4|x-5| = 12
\][/tex]
3. Divide both sides by 4 to further isolate the absolute value:
[tex]\[
|x-5| = \frac{12}{4}
\][/tex]
[tex]\[
|x-5| = 3
\][/tex]
4. Remove the absolute value by considering both cases:
[tex]\( |x-5| = 3 \)[/tex] means [tex]\( x-5 = 3 \)[/tex] or [tex]\( x-5 = -3 \)[/tex].
- Case 1: [tex]\( x-5 = 3 \)[/tex]
[tex]\[
x = 3 + 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- Case 2: [tex]\( x-5 = -3 \)[/tex]
[tex]\[
x = -3 + 5
\][/tex]
[tex]\[
x = 2
\][/tex]
Thus, the values of [tex]\( x \)[/tex] that satisfy [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
Conclusion:
The correct values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are:
[tex]\[
x = 2 \, \text{and} \, x = 8
\][/tex]
So, the answer is:
[tex]\[
x = 2, \, x = 8
\][/tex]
Here's a step-by-step solution:
1. Start with the given equation:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Isolate the absolute value term:
[tex]\[
4|x-5| + 3 - 3 = 15 - 3
\][/tex]
[tex]\[
4|x-5| = 12
\][/tex]
3. Divide both sides by 4 to further isolate the absolute value:
[tex]\[
|x-5| = \frac{12}{4}
\][/tex]
[tex]\[
|x-5| = 3
\][/tex]
4. Remove the absolute value by considering both cases:
[tex]\( |x-5| = 3 \)[/tex] means [tex]\( x-5 = 3 \)[/tex] or [tex]\( x-5 = -3 \)[/tex].
- Case 1: [tex]\( x-5 = 3 \)[/tex]
[tex]\[
x = 3 + 5
\][/tex]
[tex]\[
x = 8
\][/tex]
- Case 2: [tex]\( x-5 = -3 \)[/tex]
[tex]\[
x = -3 + 5
\][/tex]
[tex]\[
x = 2
\][/tex]
Thus, the values of [tex]\( x \)[/tex] that satisfy [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = 8 \)[/tex].
Conclusion:
The correct values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are:
[tex]\[
x = 2 \, \text{and} \, x = 8
\][/tex]
So, the answer is:
[tex]\[
x = 2, \, x = 8
\][/tex]
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Rewritten by : Jeany
