Inequalities
Lessons in this chapter
About Inequalities
Inequalities replace the equals sign with a comparison, and with it the idea that an answer can be a whole range of values rather than one.
Linear Inequalities in One Variable introduces the four symbols and what each permits. x > 5 excludes 5 itself, while x is greater than or equal to 5 includes it, and that distinction decides whether the circle on the graph is open or filled.
Write and Graph One-Step Inequalities shows the solution on a number line, which is the clearest way to see that a solution set is a range. A shaded ray with an open or closed endpoint says more in one picture than any list of values.
Solving works exactly like an equation, with one exception that 6th grade mostly sets up rather than uses: multiplying or dividing both sides by a negative number reverses the direction of the inequality. Everything else is identical.
Translation is the skill that carries into word problems. “At least” means greater than or equal to, “no more than” means less than or equal to, and getting those phrases right is usually what the question is actually testing.
Both lessons in Inequalities open as 6th grade math worksheets inside the page. Linear Inequalities in One Variable and Write and Graph One-Step Inequalities give math problems worked one at a time and marked as you go, the graphing included, which is where the open or closed circle gets decided. Free to try, with no login needed for your first 3.
Frequently asked questions
Linear Inequalities in One Variable introduces the idea that an inequality has many solutions rather than one, so the answer is a range instead of a number. Write and Graph One-Step Inequalities then asks children to turn a condition in words, such as at least 12, into a symbol, and to show the result on a number line where an open circle excludes the endpoint and a filled one includes it. The chapter sits in the Common Core domain Expressions and Equations (6.EE).
A statement that one quantity is greater or less than another, using >, <, or the greater-than-or-equal-to and less-than-or-equal-to symbols. Its solution is usually a range of values.
An open circle means the endpoint is not included, as in x > 5. A filled circle means it is included, as in x greater than or equal to 5.
Greater than or equal to. “At least 5” includes 5. “No more than 5” means less than or equal to 5, and these phrases are usually what a word problem is testing.
It is the same, with one exception: multiplying or dividing both sides by a negative number reverses the direction of the inequality sign.
Because it describes a range rather than a single point. x > 5 is true for 5.1, 6, 100 and every value above 5.