To solve this equation, we first need to convert the mixed fractions to improper fractions.

1/7 = 1/7

2 1/2 = 5/2 (2 * 2 + 1 = 5, denominator remains the same)

So, the equation becomes:

17/28 + x = -1/7 + 5/2

Next, we need to find a common denominator for the fractions on the right side of the equation, which is 14.

-1/7 becomes -2/14

5/2 becomes 35/14

Now the equation looks like this:

17/28 + x = -2/14 + 35/14

To add the fractions on the right side of the equation, we add the numerators and keep the common denominator:

17/28 + x = 33/14

Now, we need to find a common denominator for 28 and 14, which is 28.

Multiplying 33/14 by 2 (both the numerator and denominator) to have the common denominator:

33/14 * 2/2 = 66/28

So, the equation now becomes:

17/28 + x = 66/28

To solve for x, we subtract 17/28 from both sides:

x = 66/28 - 17/28

x = 49/28

Therefore, the solution to the equation is x = 49/28.