Division Property of Inequality for c < 0
Flip the inequality symbol when dividing both sides by a negative number. Apply this critical Grade 9 rule to solve inequalities involving negative division.
Key Concepts
Property For every real number $a$ and $b$, and for $c < 0$: If $a b$, then $\frac{a}{c} < \frac{b}{c}$. If $a < b$, then $\frac{a}{c} \frac{b}{c}$. Explanation Here it is again, the superstar rule! Just like with multiplication, dividing by a negative number flips the world upside down. What was greater becomes lesser. To keep your math correct in this topsy turvy situation, you absolutely have to flip the inequality sign. It's the golden rule of negative operations. Examples To solve $ 6m \ge 24$, divide by 6 and flip the sign: $\frac{ 6m}{ 6} \le \frac{24}{ 6}$, so $m \le 4$. Since $18 9$, dividing by 3 flips the sign: $\frac{18}{ 3} < \frac{9}{ 3}$ because $ 6 < 3$.
Common Questions
What is the Division Property of Inequality for c < 0 and when does it apply?
It is a rule that holds for all values in its domain. Apply it whenever you see the matching pattern in an algebraic expression or equation.
How do you apply the division property of inequality for c < 0 step by step?
Identify the pattern, substitute into the formula, simplify each part in order, and combine the results.
What mistakes should you avoid with the division property of inequality for c < 0?
Misidentifying which part of the expression the rule applies to, and forgetting conditions like nonzero bases or non-negative radicands.