To solve the equation, we need to follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the expression inside the first set of parentheses:

(2x - 3) ÷ 3 + 1

Next, we simplify the division:

(2x - 3) ÷ 3 = (2/3)x - 1

Now, we substitute this simplified expression back into the equation:

((2/3)x - 1) ÷ 5 = 20

To isolate x, we multiply both sides of the equation by 5:

5 * ((2/3)x - 1) ÷ 5 = 20 * 5

Simplifying further:

(2/3)x - 1 = 100

Next, we add 1 to both sides of the equation:

(2/3)x - 1 + 1 = 100 + 1

Simplifying further:

(2/3)x = 101

To solve for x, we multiply both sides of the equation by the reciprocal of (2/3), which is (3/2):

(3/2) * (2/3)x = (3/2) * 101

Simplifying further:

x = (3/2) * 101

Finally, we calculate the value of x:

x = 151.5