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x ≥ 3 and 3 ≤ x are equivalent. They both say that x must be at least 3. Demonstrate this.

Representing inequalities that allow equality 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 is being compared. Don't make your dot too big though. Let's not get carried away.

Example 2

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:

As before, 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.