How do I complete this formal check?

Step-by-step explanation:

The first two steps are for the purpose of eliminating fractions.  Doing so results in 4(2x - 5) = 9(x - 2), which is to be solved for x.

Perform the indicated multiplication, obtaining:

8x - 20 = 9x - 18.

Then combine like terms:  -2 = x, or

x = -2.

To complete the formal check, substitute -2 for x in the first equation.  This results in:

(1/3)(-4 - 5) = (3/4)(-2 -2), or

        -3       =        -3

... which is obviously true.