Dividing by a Negative Number
Master dividing by a negative number in Grade 9 math — Explanation Dividing by a negative is like entering a "mirror world" where everything is backward!
Key Concepts
Property When you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality symbol.
Explanation Dividing by a negative is like entering a "mirror world" where everything is backward! Greater than becomes less than, and less than becomes greater than. Forgetting to flip the sign is a super common mistake, so always double check when you see that negative sign in a multiplication or division step.
Examples Solve $ 5|x| + 10 \geq 15$. Subtract 10 to get $ 5|x| \geq 25$. Divide by $ 5$ and FLIP the sign: $|x| \leq 5$. The final answer is $ 5 \leq x \leq 5$. Solve $ 2|x 1| 8$. Divide by $ 2$ and FLIP the sign from $ $ to $<$: $|x 1| < 4$. Then solve: $ 4 < x 1 < 4$, which gives $ 3 < x < 5$.
Common Questions
What is 'Dividing by a Negative Number' in Grade 9 math?
Explanation Dividing by a negative is like entering a "mirror world" where everything is backward! Greater than becomes less than, and less than becomes greater than.
How do you solve problems involving 'Dividing by a Negative Number'?
Greater than becomes less than, and less than becomes greater than. Forgetting to flip the sign is a super common mistake, so always double-check when you see that negative sign in a multiplication or division step.
Why is 'Dividing by a Negative Number' an important Grade 9 math skill?
$$-3 + 3 \leq x - 3 + 3 \leq 3 + 3$$ $$0 \leq x \leq 6$$ The solution is all numbers between 0 and 6, inclusive.. Common mistake tip: The #1 mistake students make is forgetting to flip the inequality sign after multiplying or dividing by a negative number.