why does the inequality sign change when multiplying or dividing by a negative number? does this happen with equations?
I do not entirely know why, but yes, it does happen with equations.
(5x3 + 3)2 = (5x3)2 + (3)2 = 25x6 + 9
Determine if Louise’s answer is correct. Explain.
The inequality sign changes when multiplying or dividing by a negative number because it reflects the change in the order of the numbers being compared. Let me explain this further:
When you multiply or divide both sides of an inequality by a positive number, the inequality sign remains the same. This is because, if two numbers are in a particular order, then multiplying or dividing both of them by a positive number will preserve their order.
However, when you multiply or divide both sides of an inequality by a negative number, the inequality sign flips. This happens because multiplying or dividing by a negative number reverses the order of the numbers being compared. For example, if you have the inequality x > y, and you multiply or divide both sides by -1, you get -x < -y. The order is reversed, so the inequality sign must change.
It is important to note that this reversal of inequality does not happen in equations. In equations, both sides are equal, so multiplying or dividing both sides by any number, positive or negative, will keep the equation balanced.
To summarize:
- When multiplying or dividing both sides of an inequality by a positive number, the inequality sign remains the same.
- When multiplying or dividing both sides of an inequality by a negative number, the inequality sign flips.
I hope this explanation helps clarify why the inequality sign changes with multiplication or division by a negative number, and how it differs from equations.