Answer :
To solve the problem, we need to find the values of [tex]\(x\)[/tex] for which the function [tex]\(f(x) = 4|x - 5| + 3\)[/tex] equals 15. Let's go through the steps to find these values:
1. Set the function equal to 15:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]
2. Isolate the absolute value:
Subtract 3 from both sides to isolate the term with the absolute value:
[tex]\[
4|x - 5| = 12
\][/tex]
3. Divide by 4:
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] gives us two possible equations to solve:
- [tex]\( x - 5 = 3 \)[/tex]
- [tex]\( x - 5 = -3 \)[/tex]
5. Solve each equation:
- For [tex]\( x - 5 = 3 \)[/tex]:
[tex]\[
x = 3 + 5 = 8
\][/tex]
- For [tex]\( x - 5 = -3 \)[/tex]:
[tex]\[
x = -3 + 5 = 2
\][/tex]
6. Conclude the solution:
The values of [tex]\(x\)[/tex] for which [tex]\(f(x) = 15\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = 8\)[/tex].
Therefore, the correct values of [tex]\(x\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = 8\)[/tex].
1. Set the function equal to 15:
[tex]\[
4|x - 5| + 3 = 15
\][/tex]
2. Isolate the absolute value:
Subtract 3 from both sides to isolate the term with the absolute value:
[tex]\[
4|x - 5| = 12
\][/tex]
3. Divide by 4:
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] gives us two possible equations to solve:
- [tex]\( x - 5 = 3 \)[/tex]
- [tex]\( x - 5 = -3 \)[/tex]
5. Solve each equation:
- For [tex]\( x - 5 = 3 \)[/tex]:
[tex]\[
x = 3 + 5 = 8
\][/tex]
- For [tex]\( x - 5 = -3 \)[/tex]:
[tex]\[
x = -3 + 5 = 2
\][/tex]
6. Conclude the solution:
The values of [tex]\(x\)[/tex] for which [tex]\(f(x) = 15\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = 8\)[/tex].
Therefore, the correct values of [tex]\(x\)[/tex] are [tex]\(x = 2\)[/tex] and [tex]\(x = 8\)[/tex].
