Answer :
To solve for the values of [tex]\(x\)[/tex] where [tex]\(f(x) = 15\)[/tex] in the function [tex]\(f(x) = 4|x-5| + 3\)[/tex], follow these steps:
1. Set up the equation: Start by equating the expression for [tex]\(f(x)\)[/tex] to 15:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Isolate the absolute value: Subtract 3 from both sides to eliminate the constant term on the left side:
[tex]\[
4|x-5| = 12
\][/tex]
3. Solve for the absolute value expression: Divide both sides by 4 to solve for [tex]\(|x-5|\)[/tex]:
[tex]\[
|x-5| = 3
\][/tex]
4. Solve the absolute value equation: The equation [tex]\(|x-5| = 3\)[/tex] means there are two possible equations to solve:
- [tex]\(x-5 = 3\)[/tex]
- [tex]\(x-5 = -3\)[/tex]
5. Solve the first equation:
[tex]\[
x-5 = 3 \implies x = 3 + 5 \implies x = 8
\][/tex]
6. Solve the second equation:
[tex]\[
x-5 = -3 \implies x = -3 + 5 \implies x = 2
\][/tex]
The solutions to the given problem are [tex]\(x = 2\)[/tex] and [tex]\(x = 8\)[/tex]. These are the values for which [tex]\(f(x) = 15\)[/tex].
1. Set up the equation: Start by equating the expression for [tex]\(f(x)\)[/tex] to 15:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
2. Isolate the absolute value: Subtract 3 from both sides to eliminate the constant term on the left side:
[tex]\[
4|x-5| = 12
\][/tex]
3. Solve for the absolute value expression: Divide both sides by 4 to solve for [tex]\(|x-5|\)[/tex]:
[tex]\[
|x-5| = 3
\][/tex]
4. Solve the absolute value equation: The equation [tex]\(|x-5| = 3\)[/tex] means there are two possible equations to solve:
- [tex]\(x-5 = 3\)[/tex]
- [tex]\(x-5 = -3\)[/tex]
5. Solve the first equation:
[tex]\[
x-5 = 3 \implies x = 3 + 5 \implies x = 8
\][/tex]
6. Solve the second equation:
[tex]\[
x-5 = -3 \implies x = -3 + 5 \implies x = 2
\][/tex]
The solutions to the given problem are [tex]\(x = 2\)[/tex] and [tex]\(x = 8\)[/tex]. These are the values for which [tex]\(f(x) = 15\)[/tex].
