Inequalities are statements of INequality, relationships other than equality: less than, greater than, greater than or equal to, or less than or equal to. 

In order to write an equality you must find a relationship where one thing is smaller than or bigger than another. For example, Jed is OLDER than Ted could be written j>t. 

In order to write inequalities, it is crucial that you can READ the four inequality symbols:

< - Less than

> - Greater than

≤ - less than or equal to

≥ - greater than or equal to. 

Let's try an example. Lorelei, a car salesperson, needs to earn at least $4,200 gross pay this month. She makes $15 per hour plus a commission of 2.2% of her sales. Write an inequality that could be used to find, s, the amount of sales she would have to make in order to earn at least $4,200 gross in a month where she worked 105 hours. 

Did you notice the relationship of inequality: she needs to earn AT LEAST 4,200. 

Think about what "at least" means. 

Would she be happy with $4,200? Yes! 

How about MORE THAN $4,200? Of course; She would love that! 

But what about less than $4,200? No, way. She wouldn't be able to pay her bills. 

That is an inequality right there: her earnings ≥ 4,200. 

Now all we have to do is think of how to write "her earnings" as a math statement, and expression.

According to the problem, her earnings consist of "$15 per hour plus a commission of 2.2% of sales". We also know that she works 105 hours and sells "s" in sales. So she earns 15(105)+0.022s.

Let's put that into our inequality. 

15(105)+0.022s ≥ 4,200

Now that's going to take some practice! Watch the example problem videos below and try some practice activities.