Question

If $x>5$ and $y<-1$, then which of the following statements is true?

• A. $(x + 4y)>1$
• B. $x>-4y$
• C. $-4x<5y$
• D. None of these

Hint:

When testing inequalities, check extreme boundary values to see if the statement is always valid.

Answer 1

The Correct Option is A

We know $x>5$ and $y<-1$. Consider option (1): If $y<-1$, then $4y<-4$. Adding $x>5$ gives: $x + 4y>5 - 4 = 1$. This inequality holds for all possible values under given conditions. So (1) is always true.
Option (2): $x>-4y$. If $y = -2$, then $-4y = 8$ and $x>5$ does not guarantee $x>8$. So not always true.
Option (3): $-4x<5y$. For $x>5$, $-4x<-20$. For $y=-2$, $5y = -10$, and $-20<-10$ is true, but not guaranteed for all $y<-1$.