What is the solution of 1/3|3x-9|-5=4?

{-6, 12}

Step-by-step explanation:

Assuming that you meant (1/3), then you have:

(1/3) |3x - 9| - 5 = 4

First, let's combine the - 5 and the + 4:

(1/3) |3x - 9| = 9

Next, multipy both sides by 3 to eliminate the fraction 1/3:

|3x - 9| = 27

This absolute value equation has two separate parts:

3x - 9 = 27, and

- (3x - 9) = 27.

In the first case, we have x - 3 = 9, or x = 12.

In the second case, we have - 3x + 9 = 27, or - 3x = 18, or x = - 6.

The solution set is {-6, 12}.