I have a puzzling question.

Two problems:

2/3 t+6(less than or equal to)5 t+2 and 3/2 z - 1 (greater than or equal to) -4 z - 5

The directions I have are in order to get the variables to one side of the equation, I first need to ADD 4z to both sides in the one problem and SUBTRACT 2/3 t from both sides in the other problem.

My question is:

HOW do I know when to subtract or add? And HOW do I know which side of the inequality to start with?

4z is on the right side and is a positive number; 2/3 t is on the left side and is a negative number; however, this apparent rule does not work when the signs are opposite on either side of the inequality: for example in 4/3 u - 6 (less than) -6 u + 9.

Any help in decifering when to use which operation first would be greatly appreciated. thanks.

BTW: I am new here and am just returning to school after 35 yrs so be kind to me, K?