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.