p and q are two positive numbers such that p > 2q. Which one of the following statements is not true?

daadudaniel

3 years ago

We are given that p > 2q.

A. -p < -2q

Multiplying both sides by -1 gives p > 2q, which is true, so this statement is not the one that is not true.

B. -p > -2q

Multiplying both sides by -1 gives p < 2q, which is not true, so this statement is false.

C. -q < 2p

Dividing both sides by -2 gives q > -p/2, which is always true since both p and q are positive, so this statement is not the one that is not true.

D. q < 1/2p

Multiplying both sides by 2p gives 2pq < 1, which is always true since p > 2q, so this statement is not the one that is not true.

E. p^2 > 2q^2

Dividing both sides by q^2 gives (p/q)^2 > 2, which is true since p/q > 2, so this statement is not the one that is not true.

Therefore, the statement that is not true is (B) -p > -2q