Problem #DES-160324

Problem

Today’s topic is inequalities, expressions like $a\ge b$, or $a>b$. There are certain rules for operating inequalities: one can subtract the same number from both sides of the inequality, namely if $a\ge b$, then $a-b\ge 0$. If $a\ge b$ and $b\ge c$, then $a\ge c$. If a number $c\ge 0$, then from $a\ge b$ it follows that $ac\ge bc$. However, in case of multiplication by a negative number $c\le 0$, the inequality sign reverses: from $a\ge b$ it follows that $ac\le bc$. One should also remember that the square of any real number is non-negative.