Answer :
Sure! Let's solve the problem step-by-step.
We are given the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex] and need to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].
1. Set the equation equal to 15:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Subtract 3 from both sides to isolate the absolute value expression:
[tex]\[
4|x-5| = 12
\][/tex]
3. Divide both sides by 4 to further simplify:
[tex]\[
|x-5| = 3
\][/tex]
4. Solve the absolute value equation:
The equation [tex]\( |x-5| = 3 \)[/tex] implies two possible equations:
- [tex]\( x - 5 = 3 \)[/tex]
- [tex]\( x - 5 = -3 \)[/tex]
5. Solve each equation for [tex]\( x \)[/tex]:
- For [tex]\( x - 5 = 3 \)[/tex]:
[tex]\[
x = 3 + 5 = 8
\][/tex]
- For [tex]\( x - 5 = -3 \)[/tex]:
[tex]\[
x = -3 + 5 = 2
\][/tex]
Thus, the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex].
Therefore, the correct choice from the options given is [tex]\( x = 2, x = 8 \)[/tex].
We are given the function [tex]\( f(x) = 4|x-5| + 3 \)[/tex] and need to find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex].
1. Set the equation equal to 15:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Subtract 3 from both sides to isolate the absolute value expression:
[tex]\[
4|x-5| = 12
\][/tex]
3. Divide both sides by 4 to further simplify:
[tex]\[
|x-5| = 3
\][/tex]
4. Solve the absolute value equation:
The equation [tex]\( |x-5| = 3 \)[/tex] implies two possible equations:
- [tex]\( x - 5 = 3 \)[/tex]
- [tex]\( x - 5 = -3 \)[/tex]
5. Solve each equation for [tex]\( x \)[/tex]:
- For [tex]\( x - 5 = 3 \)[/tex]:
[tex]\[
x = 3 + 5 = 8
\][/tex]
- For [tex]\( x - 5 = -3 \)[/tex]:
[tex]\[
x = -3 + 5 = 2
\][/tex]
Thus, the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex].
Therefore, the correct choice from the options given is [tex]\( x = 2, x = 8 \)[/tex].
