The expression represents is (C) x + 999. Therefore , (C) x + 999 is correct .
Here's why:
The sum of all integers from 1 to 1000 is given as x.
We want to find the sum of all integers from 1 to 998. This means we're excluding the two numbers 999 and 1000 from the original sum.
Since we're excluding 999 and 1000, which are both positive integers, the sum will decrease.
Therefore, to get the sum of the integers from 1 to 998, we need to subtract the sum of 999 and 1000 from the original sum (x).
But, remember that we are already counting 1 in the original sum (1 to 1000). Since we want the sum from 1 to 998, we need to add 1 back to the difference of x and (999 + 1000).
Therefore, the expression that represents the sum of all integers from 1 to 998, inclusive, is:
x - (999 + 1000) + 1
Simplifying this expression, we get:
x - 2000 + 1
Combining like terms, we get:
x - 1999
However, the problem asks for the expression in terms of x, not x minus something. So, we can rewrite the expression as:
x + (-1999)
Since adding a negative number is the same as subtracting it, this is equivalent to:
x - 1999
Therefore, the final answer is (C) x + 999.
Question
If the sum of all integers from 1 to 1,000, inclusive, is x, then which expression represents the sum of all integers from 1 to 998, inclusive?
(A) x-1,999
(B) x-999
(C) x+999
(D) x+1,999