solving linear inequalities: 2/3 t + 6 <= 5 t + 2, and ....

[preachinjail]

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?

[stapel_eliz]

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

There is no one sacred set of "right" rules or orderings. Basically, you get good at recognizing "useful" steps when solving linear equations, and then you do pretty much the same steps in the same order for solving linear inequalities.

1) 2/3 t+6(less than or equal to)5 t+2

Your formatting is unclear. Do you perhaps mean the following?

. . . . .(2/3)(t + 6) < 5t + 2

Or something else?

2) 3/2 z - 1 (greater than or equal to) -4 z - 5

Is the above meant to be as follow?

. . . . .(3/2)z - 1 > -4x - 5

Or something else?

If the sign in the middle were an "equals" rather than the given signs, how would you proceed? What happens if you follow those same steps in the same order?

[preachinjail]

stapel-eliz;
you are correct concerning my formatting.
I just did not know how to make the proper inequality symbol with my keyboard.
thanks for the tip.
I know how to solve for an equation; are you saying it is the same procedure with this inequality?

[stapel_eliz]

I just did not know how to make the proper inequality symbol with my keyboard.

To learn how to format math using only text (such as here or in e-mail), try reading the lesson on formatting math as text.

I know how to solve for an equation; are you saying it is the same procedure with this inequality?

As the lesson on solving linear inequalities explained and demonstrated, yes, the techniques are almost-exactly the same.

Go for it!