1 7/9 can be converted to an improper fraction as 16/9.

Therefore, the equation becomes:

16/9 = -2 2/3

To solve this equation, we need to convert the mixed number to an improper fraction:

-2 2/3 can be converted to -8/3.

So the equation becomes:

16/9 = -8/3

To find the solution, we need to multiply both sides by 9 to get rid of the denominator:

16 = -24

This is clearly not true, so there is no solution for this equation.