Multiplication Property of Inequality for c < 0
Apply the multiplication property of inequality for negative numbers in Grade 9 algebra. Reverse the inequality sign when multiplying or dividing both sides by a negative value.
Key Concepts
Property For every real number $a$ and $b$, and for $c < 0$: If $a b$, then $ac < bc$. If $a < b$, then $ac bc$. Explanation This is the big twist! Multiplying by a negative number flips everything across zero on the number line. A bigger positive number becomes a smaller (more negative) number. Because the order reverses, you MUST flip the inequality sign to keep the statement true. Don't forget this crucial step! Examples To solve $\frac{ x}{4} < 2$, multiply by 4 and flip the sign: $( 4)\frac{ x}{4} 2( 4)$, so $x 8$. Since $5 3$, then $5( 2) < 3( 2)$ because $ 10 < 6$.
Common Questions
Why do you flip the inequality sign when multiplying by a negative number?
Multiplying by a negative reverses order on the number line. For example, 2 < 5, but -2 > -5. To maintain the correct relationship, the inequality direction must flip.
What is the multiplication property of inequality for negative numbers?
If a < b and c < 0 (negative), then a × c > b × c. The inequality reverses direction. The same rule applies to dividing by negative numbers.
How do you solve -3x < 9?
Divide both sides by -3 and reverse the inequality: x > -3. Check: x = 0 (which is > -3) gives -3(0) = 0 < 9. Correct.