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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.