An inequality is comparing two positive numbers. Explain why multiplying by a negative number on both sides of the inequality reverses the sign...

Question

anonymous · Answer

suppose you have two positive numbers like $3$ and $5$ where clearly $3<5$

anonymous · Answer

if you multiply by a negative number, say $-1$ then you have $-3$ and $-5$ so the inequality has switched 
$$3<5\
-3>-5$$

anonymous · Answer

for a more mathematical explanation 
$$a<b$$ means there is a positive number $p$ where $a+p=b$ 
if you multiply by a negative number, say $-2$  you will have 
$$-2a-2p=-b$$ making 
$$-2a=-b+2p$$ and so 
$$-2a>-2b$$

anonymous · Answer

Thank you.