To solve this equation, we can first simplify the left side of the equation by combining like terms:

(2x + 1) + (2x + 3) + (2x + 5) + ... + (2x + 99) = 2500

Grouping the terms with the same coefficient of x, we have:

(2x + 2x + 2x + ... + 2x) + (1 + 3 + 5 + ... + 99) = 2500

Simplifying further, we have:

(200x) + (1 + 3 + 5 + ... + 99) = 2500

Now, let's find the sum of the arithmetic series 1 + 3 + 5 + ... + 99. We can use the formula for the sum of an arithmetic series:

Sn = (n/2)(a1 + an)

where Sn is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term.

In this case, n = (99 - 1)/2 + 1 = 50, a1 = 1, and an = 99. Plugging these values into the formula, we get:

S = (50/2)(1 + 99) = 25(100) = 2500

Therefore, the sum of the series 1 + 3 + 5 + ... + 99 is 2500.

Substituting this value back into the equation, we have:

(200x) + 2500 = 2500

Subtracting 2500 from both sides, we get:

200x = 0

Dividing both sides by 200, we find:

x = 0

Therefore, the solution to the equation is x = 0.