Review of Inequalities

Watch this lecture series and complete the interactive exercises to review what an inequality is, what it means to find a solution set, and how to represent it on a number line.

Plotting inequalities - Questions

Answers

1.

The > is greater than symbol means "greater than and not including".

A filled circle means "including this number".

An open circle means "not including this number".

x>2 does not include 2. We can draw an open circle at 2.

Numbers to the right of 2 are greater than 2. We can draw an arrow to the right of the circle.

The graph of x>2 is:


2.

The  \leq symbol means "less than or equal to".

A filled circle means "including this number".

An open circle means "not including this number".

x \leq 5 includes 5. We can draw a filled circle at 5.

Numbers to the left of 5 are less than 5. We can draw an arrow to the left of the circle.

The graph of x \leq 5 is:


3.

The  < symbol means "less than and not including".

A filled circle means "including this number".

An open circle means "not including this number".

x < 1 does not include 1. We can draw an open circle at 1.

Numbers to the left of 1 are less than 1. We can draw an arrow to the left of the circle.

The graph of x < 1 is:


4.

The  \geq symbol means "greater than or equal to".

A filled circle means "including this number".

An open circle means "not including this number".

x \geq -1 includes -1. We can draw a filled circle at -1.

Numbers to the right of -1 are greater than -1. We can draw an arrow to the right of the circle.

The graph of x \geq -1 is: