A number, half of that number, and one-third of that number are added. The result is 22. What is the original number

A number, half of that number, and one-third of that number are added.

This statement can be expressed as:

x + (1/2) x + (1/3) x

The total is 22

x + (1/2) x + (1/3) x = 22

So let's look for x

x + (1/2) x + (1/3) x = 22

(6x + 3x + 2x) / 6 = 22

11x = 132

x = 12

So the original number is 12.