To solve this expression, we need to simplify each term separately and then subtract them.

First, let's simplify the first term: 11/50 * (- 17 1/2).

To multiply a fraction by a whole number, we multiply the numerator by the whole number and keep the denominator the same.

11/50 * (- 17 1/2) = - (11/50 * 17 1/2)

To multiply a mixed number by a fraction, we convert the mixed number to an improper fraction and then multiply.

17 1/2 = (2 * 17 + 1)/2 = 35/2

Now we can multiply:

- (11/50 * 35/2) = - (385/100) = - 3.85

Now let's simplify the second term: 11/50 * 82 1/2.

82 1/2 = (2 * 82 + 1)/2 = 165/2

Now we can multiply:

11/50 * 165/2 = 1815/100 = 18.15

Finally, we subtract the two terms:

- 3.85 - 18.15 = - 22

Therefore, 11/50 * (- 17 1/2 ) - 11/50 *82 1/2 = - 22.