Question

Find an inequality that you can use to disprove John statement. explain your thinking.

Answer 1

Try this inequality with 0 as the right side.

-x > 0

According to John, we multiply both sides by -1, and the inequality sign does not change direction, so we get this

x > 0

Let's use a number for x that makes the original inequality true.
Let x = -2.

-x > 0

-(-2) > 0

2 > 0

As you can see, -2 does work on the original equation.

Now let's try -2 in John's solution.

x > 0

-2 > 0 which is a false statement.

Now let's solve it again, but we will reverse the inequality symbol when we multiply both sides by -1.

-x > 0

x < 0

Try x = -2.

-2 < 0   which is true

Now it works.

John is incorrect.
If you multiply or divide an equation by a negative number, even if one of its sides is 0, you still must change the direction of the inequality symbol.