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: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Front

What does the inequality x < -4 represent on a number line?

Back

It represents all numbers less than -4, which is shown with an open dot at -4 and a line extending to the left.

Front

When graphing the inequality 6 > x, how is it represented on a number line?

Back

It is represented with an open dot at 6 and a line extending to the left, indicating all numbers less than 6.

Front

What does an open dot signify when graphing inequalities?

Back

An open dot signifies that the number at that point is not included in the solution set (used for < and >).

Front

What does a closed dot signify when graphing inequalities?

Back

A closed dot signifies that the number at that point is included in the solution set (used for ≤ and ≥).

Front

How do you graph the inequality x ≥ 3 on a number line?

Back

You place a closed dot at 3 and draw a line extending to the right, indicating all numbers greater than or equal to 3.

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 can you check if a number is a solution to an inequality?

Back

Substitute the number into the inequality and see if the statement is true.

Front

What is the solution set of the inequality x < 2?

Back

The solution set includes all real numbers less than 2.