What is the expression x - 4 represents a negative integer. what integers could x represent?

The expression x-4 will come out to be a negative integer. That means X has to be something that when 4 is taken away from it, the answer is still negative.

Let's try 5.
5-4 is 1. Is 1 negative? No, so that doesn't work.
4-4 is 0. 0 isn't negative either, so that doesn't work.
3-4 is -1. Is -1 negative? YES! Let's try it for 2 as well, just to be safe.
2-4 is -2. Still negative.

X can be anything less than 4. 

x=number of shirts
y=number of DVDs
We can suggest the following system of inequalities.
30x+12y<175

We solve for x:
maxmimun number of y: y<175/12; y<14
30x+12y<175
30x<175-12y
x<(175-12 y)/30           " y" can be:0,1,2,,14

Answer 1= the solution for shirts would be x<(175-12y)/30   ;  
"y " can be:0,1,2,...,14

We solve for y;
 maximum number of DVDs:    x<175/30<5

30x+12y<175
12y<175-30x
y<(175-30x)/12;        "x" can be: 0,1,2,3,4,5.

answer 2: the solutions for DVDs would be: y<(175-30x)/12; 
"x" can be: 0,1,2,3,4,5.