# Inequalities with Multiplication and Division

## Key Questions

• There are only a few rules:

You may add or subtract the same from both sides

You may multiply or divide by the same on both sides, BUT:

If you multiply/divide by a negative number the sign changes direction $> \to <$ and vice versa.

Simple example (mutiplied by $- 1$)
$- x < - 2 \to x > 2$

• When you multiply or divide by a negative number the order of the quantities is reversed. You can verify this by considering a simple example. We know that $1 < 2$, but when you multiply both numbers by $- 1$, then the direction of the inequality is reversed $- 1 > - 2$.

I hope that this was convincing enough.

• This key question hasn't been answered yet.

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