Question

Why does the inequality sign change when both sides are

multiplied or divided by a negative number? Does this happen with equations? Why or why not?

Answer 1

It does not happen with equations because there is no one side or the other is to the right or left about an equation.
To convince yourself of how this works draw a number line.
Mark 3 on it and 4 on it.
then no doubt 3 is to the left, less than 4
so 3<4
now multiply both sides by -1 (change the signs of the numbers.)
-3 ? -4
mark those two on your graph.
Notice that -3 is to the RIGHT of -4.
In other words the mirror image reverses right and left.
and now:
-3>-4