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Sometimes two objects may not be equal, but instead  the objectsmay be greater than, or less than one another. This is where inequality signs come in handy.

A Quick Review of Inequality Signs

> Greater Than

≥  Greater Than and Equal To

< Less than

≤ Less Than and Equal To

When ever multiply or divide both sides of an equation by a negative number you must flip the sign.

Why?

Let's take  1 < 2 and multiply both sides by -3.

1 x -3 = -1 < 2 x -3 = -6

-3 < -6

After multiplying both sides by -3 the equation is not true, so you need to flip the sign.

-3 > -6

The rule is anytime you multiply or divide both sides by a negative number you need to flip the inequality sign.

Lets work one example

6 - 5x  >   21

Subtract 6 from both sides
-5x > 15

Divide each side by -5

x > -3

Flip the sign
x < -3

So in summary

When working with inequalities, anytime you MULTIPLY or DIVIDE both sides of an inequality by a NEGATIVE NUMBER you need to flip the signs.