To solve the equation, we can start by simplifying both sides:

l5/3 - xl - l5/6l = l - 5/9l

To simplify the left side, we need to find a common denominator for the fractions. The least common multiple of 3 and 6 is 6, so we can rewrite the equation as:

(10/6)l - xl - (5/6)l = l - (10/9)l

Now, we can combine like terms on both sides:

[(10/6) - (5/6)]l - xl = (1 - 10/9)l

(5/6)l - xl = (9/9 - 10/9)l

(5/6)l - xl = (-1/9)l

Next, we can move all the terms with "l" to one side of the equation:

(5/6 - x + 1/9)l = 0

Now, for the equation to be true, the coefficient of "l" must be zero. Therefore, we have:

5/6 - x + 1/9 = 0

To solve for "x," we can multiply through by the least common multiple of 6 and 9, which is 18:

(18)(5/6 - x + 1/9) = (18)(0)

(15 - 18x + 2) = 0

17 - 18x = 0

-18x = -17

x = 17/18

Therefore, the solution to the equation is x = 17/18.