Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What symbols are used to represent inequalities?

Back

The symbols used to represent inequalities are: > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).

Front

How do you graph the inequality r ≥ -6?

Back

To graph r ≥ -6, draw a number line, place a closed dot on -6 to indicate that -6 is included, and shade to the right to show all values greater than -6.

Front

What does a closed dot on a graph indicate?

Back

A closed dot indicates that the number at that point is included in the solution set of the inequality.

Front

What does an open dot on a graph indicate?

Back

An open dot indicates that the number at that point is not included in the solution set of the inequality.

Front

How do you write the inequality for a graph that shows all values greater than 5?

Back

The inequality for a graph that shows all values greater than 5 is written as x > 5.

Front

What is the inequality represented by the number line graph that shows all values less than -4?

Back

The inequality represented is x < -4.

Front

Which graph corresponds to the inequality 2 > p?

Back

The graph that corresponds to the inequality 2 > p will show an open dot at 2 and shading to the left.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (>, <) do not include the boundary point, while non-strict inequalities (≥, ≤) do include the boundary point.

Front

How do you determine the direction of shading when graphing an inequality?

Back

The direction of shading is determined by the inequality symbol: shade to the right for > or ≥, and shade to the left for < or ≤.