Answer :
To solve the equation [tex]\( f(x) = 4|x-5| + 3 = 15 \)[/tex] for [tex]\( x \)[/tex], follow these steps:
1. Set up the equation: Start with the function given:
[tex]\[
f(x) = 4|x-5| + 3
\][/tex]
We want to find when [tex]\( f(x) = 15 \)[/tex].
2. Subtract 3 from both sides:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
Subtract 3 from both sides to isolate the absolute value term:
[tex]\[
4|x-5| = 12
\][/tex]
3. Divide by 4:
Divide both sides by 4 to further simplify:
[tex]\[
|x-5| = 3
\][/tex]
4. Set up two equations: The equation [tex]\( |x-5| = 3 \)[/tex] can be split into two separate equations to remove the absolute value:
- First equation:
[tex]\[
x - 5 = 3
\][/tex]
- Second equation:
[tex]\[
x - 5 = -3
\][/tex]
5. Solve the first equation:
- Add 5 to both sides:
[tex]\[
x = 8
\][/tex]
6. Solve the second equation:
- Add 5 to both sides:
[tex]\[
x = 2
\][/tex]
The values of [tex]\( x \)[/tex] that make [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex].
1. Set up the equation: Start with the function given:
[tex]\[
f(x) = 4|x-5| + 3
\][/tex]
We want to find when [tex]\( f(x) = 15 \)[/tex].
2. Subtract 3 from both sides:
[tex]\[
4|x-5| + 3 = 15
\][/tex]
Subtract 3 from both sides to isolate the absolute value term:
[tex]\[
4|x-5| = 12
\][/tex]
3. Divide by 4:
Divide both sides by 4 to further simplify:
[tex]\[
|x-5| = 3
\][/tex]
4. Set up two equations: The equation [tex]\( |x-5| = 3 \)[/tex] can be split into two separate equations to remove the absolute value:
- First equation:
[tex]\[
x - 5 = 3
\][/tex]
- Second equation:
[tex]\[
x - 5 = -3
\][/tex]
5. Solve the first equation:
- Add 5 to both sides:
[tex]\[
x = 8
\][/tex]
6. Solve the second equation:
- Add 5 to both sides:
[tex]\[
x = 2
\][/tex]
The values of [tex]\( x \)[/tex] that make [tex]\( f(x) = 15 \)[/tex] are [tex]\( x = 8 \)[/tex] and [tex]\( x = 2 \)[/tex].
