The variables p and q have the same numerical value but the opposite sign; that is, one is positive and the other is negative. If
-3*p + 4*q is positive, what can you say about p and q?
if p>0, then q<0 and -3p+4q is negative.
So, p<0 and q>0
-3p > 0
4q > 0
so -3p+4q > 0
To determine what we can say about the variables p and q, we need to analyze the given expression -3*p + 4*q being positive when p and q have the same numerical value but opposite signs.
Let's start by assigning a value to one of the variables, say p. Since p and q have the same numerical value but opposite signs, we can let p be any positive number, such as p = 3.
Now, let's substitute this value of p into the expression and see what happens:
-3*3 + 4*q = -9 + 4*q
From here, we know that -9 is negative because it has a negative sign, and we want the expression to be positive. To achieve a positive result, 4*q must be greater than -9.
To make it clearer, let's divide both sides of the inequality by 4:
4*q > -9 / 4
This simplifies to:
q > -2.25
So, from our calculations, we can conclude that if p is positive, then q must be greater than -2.25.
In summary, when p and q have the same numerical value but opposite signs and the expression -3*p + 4*q is positive, we can say that p is positive and q is greater than -2.25.