There is one important difference between solving equations and solving inequalities. When dividing or multiplying the inequality by a negative number, the inequality symbol must be reversed or flipped.
Consider the following example to understand why the inequality symbol is reversed. The inequality
is a true statement. Multiplying both sides by -1
Notice that -5
is smaller than -2.
Thus, the inequality symbol that makes this a true statement is >.
Therefore, when multiplying or dividing an inequality by a negative number, the inequality symbol must be reversed.