Example Card: Dividing by a Negative Number

This problem looks straightforward, but a hidden rule about division can change the final answer completely. Let's apply the Division Property of Inequality for $c < 0$.

Example Problem Solve, graph, and check the solution for the inequality $ 5m \ge 12$.

Step by Step 1. Start with the given inequality. $$ 5m \ge 12 $$ 2. To solve for $m$, we will divide both sides by $ 5$. Remember to reverse the inequality symbol because we are dividing by a negative number. $$ \frac{ 5m}{ 5} \le \frac{12}{ 5} \quad \text{Division Property of Inequality for } c < 0 $$ 3. Simplify the expression and write the solution as a mixed number. $$ m \le 2\frac{2}{5} \quad \text{Simplify.} $$ 4. Graph the solution on a number line. Use a closed circle at $ 2\frac{2}{5}$ with an arrow pointing to the left to include all numbers less than or equal to it.