To solve this equation, we first need to simplify the expression inside the parentheses:

1 2/3x - (1.5x - 2)

= 1 2/3x - 1.5x + 2 (distributing the negative sign)

Next, we combine like terms:

1 2/3x - 1.5x + 2 = 2.6

To add the mixed number and the fraction, we need to find a common denominator. Converting the mixed number to a fraction:

1 2/3 = 5/3

So, our equation becomes:

5/3x - 1.5x + 2 = 2.6

Combine like terms:

(5/3 - 1.5)x + 2 = 2.6

To find a common denominator between 3 and 2, we multiply 3 and 2 to get 6. So, we rewrite the equation as:

(10/6 - 9/6)x + 2 = 2.6

(1/6)x + 2 = 2.6

Subtract 2 from both sides:

(1/6)x = 0.6

Now, multiply both sides by 6 to solve for x:

x = 0.6 * 6
x = 3

Therefore, the solution to the equation is x = 3.