To solve this equation, we need to find the value of x that satisfies the equation:

[x + 1] + [x + 2] + ... + [20] = 1210

First, let's simplify the equation by expanding the summation:

[x + 1] + [x + 2] + ... + [20] = 1210
(x + 1) + (x + 2) + ... + 20 = 1210

Now, let's combine like terms:

2x + 1 + 2 + ... + 20 = 1210

To find the sum of consecutive numbers from 1 to n, we can use the formula:

Sum = (n/2)(first term + last term)

In this case, the first term is 1 and the last term is 20, so we have:

Sum = (20/2)(1 + 20) = 10(21) = 210

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

2x + 210 = 1210

Subtract 210 from both sides:

2x = 1210 - 210
2x = 1000

Divide both sides by 2:

x = 1000/2
x = 500

Therefore, the value of x that satisfies the equation is 500.