# 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.

Use the order of operations in reverse and remember that dividing or multiplying by a negative reverses the inequality

#### Explanation:

The order of operations is PEMDAS in reverse it is PESADM ( if you lose your cell phone in PE you are a SAD M(am)

Remember multiply or dividing by a negative reverses the value of the quality being divided or multiplied.

$+ \times - = -$

$\left(\frac{-}{-}\right) = +$

 < xx (-) = > y  >/(-) = <#

Just do the order of operations in reverse as in solving an equation always doing the opposite. Then remember to reverse the inequality sign whenever the inequality is multiplied or divided by a negative.