Answer :
We are given the function
[tex]$$
f(x) = 4|x-5| + 3
$$[/tex]
and we need to find the values of [tex]$x$[/tex] for which [tex]$f(x) = 15$[/tex]. Follow these steps:
1. Write the equation:
[tex]$$
4|x-5| + 3 = 15.
$$[/tex]
2. Subtract [tex]$3$[/tex] from both sides to isolate the absolute value term:
[tex]$$
4|x-5| = 15 - 3 = 12.
$$[/tex]
3. Divide by [tex]$4$[/tex] on both sides:
[tex]$$
|x-5| = \frac{12}{4} = 3.
$$[/tex]
4. Solve the absolute value equation:
The equation [tex]$|x-5| = 3$[/tex] means that either:
[tex]$$
x - 5 = 3 \quad \text{or} \quad x - 5 = -3.
$$[/tex]
For [tex]$x-5 = 3$[/tex]:
[tex]$$
x = 5 + 3 = 8.
$$[/tex]
For [tex]$x-5 = -3$[/tex]:
[tex]$$
x = 5 - 3 = 2.
$$[/tex]
So, the solutions are [tex]$x=2$[/tex] and [tex]$x=8$[/tex].
[tex]$$
f(x) = 4|x-5| + 3
$$[/tex]
and we need to find the values of [tex]$x$[/tex] for which [tex]$f(x) = 15$[/tex]. Follow these steps:
1. Write the equation:
[tex]$$
4|x-5| + 3 = 15.
$$[/tex]
2. Subtract [tex]$3$[/tex] from both sides to isolate the absolute value term:
[tex]$$
4|x-5| = 15 - 3 = 12.
$$[/tex]
3. Divide by [tex]$4$[/tex] on both sides:
[tex]$$
|x-5| = \frac{12}{4} = 3.
$$[/tex]
4. Solve the absolute value equation:
The equation [tex]$|x-5| = 3$[/tex] means that either:
[tex]$$
x - 5 = 3 \quad \text{or} \quad x - 5 = -3.
$$[/tex]
For [tex]$x-5 = 3$[/tex]:
[tex]$$
x = 5 + 3 = 8.
$$[/tex]
For [tex]$x-5 = -3$[/tex]:
[tex]$$
x = 5 - 3 = 2.
$$[/tex]
So, the solutions are [tex]$x=2$[/tex] and [tex]$x=8$[/tex].
