Given the function f(x) = 3|x - 2| + 6, for what values of x is f(x) = 18?

Solution:

Given: Function f(x) = 3|x - 2| + 6

In order to determine the value of x put f(x) = 18

3|x - 2| + 6 = 18

Subtract 6 on both sides

3|x - 2| + 6 - 6 = 18 - 6

3|x - 2| = 12

Divide both sides by 3

|x - 2| = 4

We know that an absolute value function contains two x values

|x - 2| = 4

x - 2 = ± 4

So we get

x - 2 = 4 or x - 2 = - 4

x = 4 + 2 or x = - 4 + 2

x = 6 or x = -2

Therefore, the values of x are 6 or -2.

---

Given the function f(x) = 3|x - 2| + 6, for what values of x is f(x) = 18?

Summary:

The values of x are 6 or -2 for the given function f(x) = 3|x - 2| + 6, for f(x) = 18.