To solve the equation, we can start by taking the cube root of both sides:

∛((2x - 1)^3) = ∛(8/27)

Simplifying the cube root of the left side:

2x - 1 = ∛(8/27)

Next, we can simplify the cube root of the right side:

2x - 1 = ∛(2^3/3^3)

Since 8 = 2^3 and 27 = 3^3, we can rewrite the equation as:

2x - 1 = ∛(2^3)/∛(3^3)

Taking the cube root of 2^3 and 3^3:

2x - 1 = 2/3

Now, we can isolate the variable x by adding 1 to both sides:

2x = 2/3 + 1

2x = 2/3 + 3/3

2x = 5/3

Finally, divide both sides by 2 to solve for x:

x = (5/3) / 2

x = 5/6

Therefore, the solution to the equation (2x - 1)^3 = 8/27 is x = 5/6.