1. The problem is to solve an inequality while keeping the greater than or less than symbol intact. 2. When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality symbol. 3. For example, if we have $-2x > 6$, dividing both sides by $-2$ gives $x < \frac{6}{-2}$ because the inequality flips. 4. Simplify the fraction: $$x < \cancel{\frac{6}{-2}} = -3$$ 5. So the solution is $x < -3$. 6. Always keep the inequality symbol and flip it only when multiplying or dividing by a negative number. 7. This ensures the solution set is correctly represented.