Mathematics help

Question

If p<-3 and q>-5,then the value of p-q...

A.Greater than 9
B.Greater than 7
C.Less than 8
D.Less than 2

Answer 1

First of all, notice that p - q is the same as p + (-q).  We'll need this later.

 

You can take the statement q>-5 and multiply both sides by -1.  With equations, you can almost always do the same operation to both sides and the equation is still true.  You can do similar things with inequalities, but if you multiply or divide both sides by a negative number, you have to REVERSE the direction of the inequality.

 

So q >- 5 is the same as -q < 5

 

Now you have two inequalities that point in the same direction:

 

p < -3

-q < 5

 

That means that you can add the two inequalities together and the result will still be true.  That gives you:

 

p + -q < 2

 

But remember what we said at the beginning.  p + -q is the same as p - q.  So that means that you have:

 

p - q < 2

 

So the answer is D.