Non-Strict Inequalities Examples

The inequalities x ≥ 3 and 3 ≤ x are equivalent, since they both say that x must be at least 3. Demonstrate this using a number line.

To represent the inequality 3 ≤ x we draw a number line labeled with the name of the variable, and put a big dot at 3:

Then we shade all values on the number line greater than (to the right of) 3, since all these values are also solutions to the inequality.

Representing non-strict inequalities on the number line is similar to representing strict inequalities on the number line. Instead of drawing an open circle, we draw a big (closed) dot to show that the variable can equal the number to which it's being compared. Don't make your dot too big though. Let's not get carried away.