To solve this equation, we first need to simplify the left side:

2 1/2 = 5/2

Now let's rewrite the equation with the simplified values:

5/2 × 1 1/5 - 7/18 = 1 5/6

Next, convert the mixed number to an improper fraction:

1 1/5 = 6/5

Now the equation is:

5/2 × 6/5 - 7/18 = 1 5/6

Simplify the fractions in the equation:

5/2 × 6/5 = 3/1 = 3

The equation now becomes:

3 - 7/18 = 1 5/6

To subtract the fractions, we need to find a common denominator which in this case is 18:

54/18 - 7/18 = 47/18

Therefore, the final equation will be:

47/18 = 1 5/6