To solve this equation, we first need to simplify both sides by dividing.

Starting with the left side:

(1.2x - 5) / 6

Distribute the division by 6:

1.2x / 6 - 5 / 6

Simplify:

0.2x - 5/6

Now moving on to the right side:

(2.2x + 3) / 3

Distribute the division by 3:

2.2x / 3 + 3 / 3

Simplify:

0.733x + 1

So, our equation becomes:

0.2x - 5/6 = 0.733x + 1

Now we need to solve for x.

First, get rid of the denominator by multiplying both sides by 6:

6(0.2x - 5/6) = 6(0.733x + 1)

1.2x - 5 = 4.398x + 6

Now, combine like terms:

1.2x - 4.398x = 5 + 6

-3.198x = 11

Finally, solve for x:

x = -3.44