To solve this equation, we can start by simplifying the expression on the left side:

1/3 * (-4/9 * x + 1) = -5/6

First, let's simplify the expression inside the parentheses:

-4/9 * x + 1

To multiply fractions, we multiply the numerators together and the denominators together:

(-4 * x) / (9 * 1) + 1

Simplifying further:

-4x / 9 + 1

Now, let's substitute this simplified expression back into the original equation:

1/3 * (-4x / 9 + 1) = -5/6

To distribute the 1/3 to both terms inside the parentheses:

(1/3) * (-4x / 9) + (1/3) * 1 = -5/6

Simplifying further:

-4x / 27 + 1/3 = -5/6

To add fractions, we need a common denominator. The least common multiple of 27 and 3 is 27. So, let's convert the fractions to have a denominator of 27:

(-4x * 3) / (27 * 3) + (1 * 9) / (3 * 9) = -5/6

Simplifying further:

-12x / 81 + 9 / 27 = -5/6

-12x / 81 + 9 / 27 can be simplified to:

-4x / 27 + 1/3

Now, let's substitute this simplified expression back into the equation:

-4x / 27 + 1/3 = -5/6

Now, we can multiply both sides of the equation by the common denominator, which is 27 * 6 = 162:

(162) * (-4x / 27 + 1/3) = (162) * (-5/6)

Simplifying further:

-4x * 6 + 27 * 1 = -5 * 162

-24x + 27 = -810

Next, let's isolate the variable by subtracting 27 from both sides:

-24x + 27 - 27 = -810 - 27

Simplifying further:

-24x = -837

Finally, divide both sides by -24 to solve for x:

(-24x) / -24 = (-837) / -24

Simplifying further:

x = 34.875

Therefore, the solution to the equation is x = 34.875.