Hi,
Using the following steps, one need not worry about the 'reverses inequality' rule
-5x/3 + 2 > 12
-5x/3 + 2 + 5x/3 > 12 + 5x/3
2 > 12 + 5x/3
-6 > x
Using this method of solving,(multiplying/dividing by negative number) Yes,reverses the inequality sign
-5x/3 + 2 > 12
x < -6