Answer :
Sure, let's find the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] for the given function [tex]\( f(x) = 4|x-5| + 3 \)[/tex].
1. Start with the function equation:
[tex]\[
f(x) = 4|x-5| + 3
\][/tex]
2. Set [tex]\( f(x) = 15 \)[/tex]:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
3. Subtract 3 from both sides to isolate the absolute value expression:
[tex]\[
4|x-5| = 12
\][/tex]
4. Divide both sides by 4:
[tex]\[
|x-5| = 3
\][/tex]
5. Solve the absolute value equation, which gives two cases:
- Case 1: [tex]\( x-5 = 3 \)[/tex]
[tex]\[
x-5 = 3
\][/tex]
[tex]\[
x = 5 + 3
\][/tex]
[tex]\[
x = 8
\][/tex]
- Case 2: [tex]\( x-5 = -3 \)[/tex]
[tex]\[
x-5 = -3
\][/tex]
[tex]\[
x = 5 - 3
\][/tex]
[tex]\[
x = 2
\][/tex]
6. Thus, the solutions are:
[tex]\[
x = 2 \quad \text{and} \quad x = 8
\][/tex]
By solving the equation [tex]\( 4|x-5| + 3 = 15 \)[/tex], we find that the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x=2 \)[/tex] and [tex]\( x=8 \)[/tex], so the correct answer is:
[tex]\[
x=2, x=8
\][/tex]
1. Start with the function equation:
[tex]\[
f(x) = 4|x-5| + 3
\][/tex]
2. Set [tex]\( f(x) = 15 \)[/tex]:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
3. Subtract 3 from both sides to isolate the absolute value expression:
[tex]\[
4|x-5| = 12
\][/tex]
4. Divide both sides by 4:
[tex]\[
|x-5| = 3
\][/tex]
5. Solve the absolute value equation, which gives two cases:
- Case 1: [tex]\( x-5 = 3 \)[/tex]
[tex]\[
x-5 = 3
\][/tex]
[tex]\[
x = 5 + 3
\][/tex]
[tex]\[
x = 8
\][/tex]
- Case 2: [tex]\( x-5 = -3 \)[/tex]
[tex]\[
x-5 = -3
\][/tex]
[tex]\[
x = 5 - 3
\][/tex]
[tex]\[
x = 2
\][/tex]
6. Thus, the solutions are:
[tex]\[
x = 2 \quad \text{and} \quad x = 8
\][/tex]
By solving the equation [tex]\( 4|x-5| + 3 = 15 \)[/tex], we find that the values of [tex]\( x \)[/tex] for which [tex]\( f(x) = 15 \)[/tex] are [tex]\( x=2 \)[/tex] and [tex]\( x=8 \)[/tex], so the correct answer is:
[tex]\[
x=2, x=8
\][/tex]
