Introduction to Inequalities:

Some numbers get no respect. Take 0, for example, who usually gets the short end of the stick. In fact, people treat him like he’s not even there; he's a complete nobody, a nothing. But this isn’t quite what inequalities are about. Besides, 0 is actually much larger than a lot of other numbers. 

He just doesn’t throw it back in their faces. He’s bigger than that.

Inequalities are mathematical statements that compare quantities. If a problem asks you to solve for the inequality in an equation such as this one:

-7 __ 3

... you would insert a "<" (less than) symbol in the blank to indicate that the 3 is the larger of the two numbers. You can remember this in one of two ways: think of the symbol as the mouth of a hungry alligator that would prefer to go after the bigger meal, or an arrow that is pointing and laughing at the smaller number. Either way, the numbers won’t be getting out of this situation entirely unscathed.

You’ll also encounter inequality problems that involve variables, as well as ones that feature "greater than or equal to" and "less than or equal to" symbols. These are just like the hungry alligator/pointing finger (...put together, that could end badly), except they like hanging out at the bottom of an equals sign.

4x – 5 ≥ 10

To solve a problem like as this one, add 5 to both sides and then divide both by 4 in order to isolate the variable. Because if anyone’s going to get eaten, it might as well be the lone letter. It’s every number for herself around here.

 
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