To solve this expression, we need to follow the order of operations (PEMDAS/BODMAS).

First, let's simplify the division: -3/4 ÷ 14/17.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
So, -3/4 ÷ 14/17 = -3/4 * 17/14 = -51/56.

Now, let's add the fractions: -3/4 + 11/14 + 7/2 + -51/56.
To add fractions, we need to find a common denominator.
The common denominator for 4, 14, 2, and 56 is 56.

Converting all fractions to have a denominator of 56:
-3/4 = -42/56
11/14 = 22/28 = 22/28 * 2/2 = 44/56
7/2 = 7/2 * 28/28 = 196/56
-51/56 = -51/56

Now, we can add the fractions:
-42/56 + 44/56 + 196/56 - 51/56 = ( -42 + 44 + 196 - 51 ) / 56 = 147/56.

Therefore, -3/4 + 11/14 + 7/2 + -3/4 ÷ 14/17 = 147/56.