Question

Counterexamples John says that if one side of an inequality is 0, you

don’t have to reverse the inequality symbol when you multiply or divide
both sides by a negative number. Find an inequality that you can use
to disprove John’s statement. Explain your thinking.

Answer 1

He may be wrong. If he was wrong, this is the example.

0 < -10x

If we were to divide both sides by -10, even though the answer would be undefined or just end up as zero, it is just a common rule to always flip the sign whenever you divide or multiply by a negative.

Don't quote me on it, but I think I'm right.

Hope this helped!

Answer 2

Answer with explanation:

Mathematically , john's statement is wrong which is:→ if one side of an inequality is 0, you don’t have to reverse the inequality symbol when you multiply or divide both sides by a negative number.

Counterexample :Consider an example

→ 4x ≥ 0, where x is a positive integer.

If we multiply or divide both sides by , -1, the inequality would result into

→ -4x ≤ 0

This transformed inequality is valid only when ,x is a Positive Integer.Here after multiplying by negative integer ,if we will not change the inequality sign, it will be an invalid Inequality.