Opposing Squares Problem from Question Bank - Algebra

[allison.m.marshall]

Regarding problem #17 in Question Bank - Algebra (Equations, Inequalities, & VICs), why is it that, for (1) if pq<0 we KNOW "Is p < q?"?

[jnelson0612]

Regarding problem #17 in Question Bank - Algebra (Equations, Inequalities, & VICs), why is it that, for (1) if pq<0 we KNOW "Is p < q?"?

Sure. Let's go back to the question:

Is (p^2)q > p(q^2)?

We can rewrite this as "is p(pq) > q(pq)?" There's our rephrased question.

It's tempting to divide by pq, but we don't know if pq is positive (leave sign as is when dividing) or negative (flip the sign when dividing).

Now, statement 1 says pq < 0, or it's negative. NOW we can divide both sides of our question by pq, and since it's negative we flip the sign.

Thus, p < q.

Let us know if you need more help!