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Answer :
To find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] in the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex], follow these steps:
1. Set the function equal to 15:
[tex]\( f(x) = 15 \)[/tex]
So, [tex]\( 4|x - 5| + 3 = 15 \)[/tex].
2. Isolate the absolute value expression:
Subtract 3 from both sides:
[tex]\( 4|x - 5| = 12 \)[/tex].
3. Divide by 4 to solve for the absolute value:
[tex]\( |x - 5| = 3 \)[/tex].
4. Solve the absolute value equation:
The equation [tex]\( |x - 5| = 3 \)[/tex] implies two possible cases:
- Case 1: [tex]\( x - 5 = 3 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\( x = 5 + 3 = 8 \)[/tex].
- Case 2: [tex]\( x - 5 = -3 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\( x = 5 - 3 = 2 \)[/tex].
Therefore, the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex]. This corresponds to the answer choice [tex]\( x = 2, x = 8 \)[/tex].
1. Set the function equal to 15:
[tex]\( f(x) = 15 \)[/tex]
So, [tex]\( 4|x - 5| + 3 = 15 \)[/tex].
2. Isolate the absolute value expression:
Subtract 3 from both sides:
[tex]\( 4|x - 5| = 12 \)[/tex].
3. Divide by 4 to solve for the absolute value:
[tex]\( |x - 5| = 3 \)[/tex].
4. Solve the absolute value equation:
The equation [tex]\( |x - 5| = 3 \)[/tex] implies two possible cases:
- Case 1: [tex]\( x - 5 = 3 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\( x = 5 + 3 = 8 \)[/tex].
- Case 2: [tex]\( x - 5 = -3 \)[/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\( x = 5 - 3 = 2 \)[/tex].
Therefore, the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex]. This corresponds to the answer choice [tex]\( x = 2, x = 8 \)[/tex].
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