(x + 1) + (x + 2) + (x + 3) + ... + (x + 1000) = 5750
<=> 100x + (1 + 2 + 3 + ... + 100) = 5750
<=> 100x + (1 + 100) x 50 = 5750
<=> 100x + 101 x 50 = 5750
<=> 100x + 5050 = 5750
<=> 100x = 5750 - 5050
<=> 100x = 700
<=> x = 7
(x + 1) + (x + 2) + (x + 3) + ... + (x + 1000) = 5750
<=> 100x + (1 + 2 + 3 + ... + 100) = 5750
<=> 100x + (1 + 100) x 50 = 5750
<=> 100x + 101 x 50 = 5750
<=> 100x + 5050 = 5750
<=> 100x = 5750 - 5050
<=> 100x = 700
<=> x = 7