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 $\text{-}1$ results in Notice that $\text{-}5$ is smaller than $\text{-}2.$ 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.