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

x = - 2, x = 6

Step-by-step explanation:

Given f (x) = 18 we require to solve

3 | x - 2 | + 6 = 18 (subtract 6 from both sides)

3 | x - 2 | = 12 (divide both sides by 3)

| x - 2 | = 4

The absolute value function always returns a positive value, however, the expression inside can be positive or negative, thus

x - 2 = 4 (add 2 to both sides)

x = 6

OR

- (x - 2) = 4

- x + 2 = 4 (subtract 2 from both sides)

- x = 2 (multiply both sides by - 1)

x = - 2

As a check substitute these values into the left side of the equation and if equal to the right side then they are the solutions

x = 6 → 3|6 - 2| + 6 = 3|4| + 6 = 3 (4) + 6 = 12 + 6 = 18 ← True

x = - 2 → 3| - 2 - 2| + 6 = 3|-4| + 6 = 3 (4) + 6 = 12 + 6 = 18 ← True

Hence solutions are x = - 2, x = 6