Writing Inequalities

Unequal Relationships

There are more types of relationships than equality. Mathematical expressions can be less than or greater than each other as well.

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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.


Writing Inequalities (Beginner)

Practice writing simple inequalities that relate one variable to a single number.

Practice writing inequalities from word problems with this practice set from Khan Academy.



Beginning 1

Experienced 1

Experienced 2

Experienced 3

Advanced 1