I want to make sure that I am on the right track with these inequalities. I cannot figure how to type the mathmatical symbols in the text, so I've typed words instead in some cases. Thanks for the help!

1) The set notation for the inequality: 1/4y - 1/3 < y + 2 = ? ( I've come up with {y|y > -28/9} is this right?

2) The set notation for the inequality: 3 is less than or equal to 4 + 3x/2 is less than or equal to 2. Is the answer 0??

3) 4 < -z -4 < 11; I come up with: {z|-8 > z >-15} Is this right?

2. Originally Posted by jay1
I want to make sure that I am on the right track with these inequalities. I cannot figure how to type the mathmatical symbols in the text, so I've typed words instead in some cases. Thanks for the help!

1) The set notation for the inequality: 1/4y - 1/3 < y + 2 = ? ( I've come up with {y|y > -28/9} is this right? Correct

2) The set notation for the inequality: 3 is less than or equal to 4 + 3x/2 is less than or equal to 2. Is the answer 0?? 3 less or equal 2?! sounds like the null set. Are you sure that you copied this correctly?

3) 4 < -z -4 < 11; I come up with: {z|-8 > z >-15} Is this right? Correct.
.

3. Here's the inequality again: 3 is less than or equal to 4 + 3x/2 is less than or equal to 2. I need the result of this in set notation. My assumption is the answer is 0, but I could be wrong?
(I couldn't type the symbol for less than or equal to, hence typing the words)

4. Originally Posted by jay1
Here's the inequality again: 3 is less than or equal to 4 + 3x/2 is less than or equal to 2. I need the result of this in set notation. My assumption is the answer is 0, but I could be wrong?
(I couldn't type the symbol for less than or equal to, hence typing the words)
Yes, you are wrong. This is because you are not looking for a single solution, but the set of all solutions. 0 is a solution. I think that you mean to say that there is no solution.

5. Yes, that is what I meant, no solution. Is the answer no solution?

6. Originally Posted by jay1
Yes, that is what I meant, no solution. Is the answer no solution?
Yes, but how would you describe "no solution" in set builder notation?

7. Thanks for all of the help; I am having trouble graphing some of these. For example, how do I graph the solution set of x + 2y is less than or equal to 3, and x + 2y is less than or equal to 4?
How do I graph the inequality 3x is less than or equal to -4y - 4?? Are these lines graphed horizontally or diagonally?