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

What does a closed circle on a graph indicate?

Back

A closed circle on a graph indicates that the endpoint is included in the solution set, which occurs for inequalities with ≥ or ≤.

Front

What does an open circle on a graph indicate?

Back

An open circle on a graph indicates that the endpoint is not included in the solution set, which occurs for inequalities with > or <.

Front

How do you solve the inequality 3x + 7 < 22?

Back

To solve 3x + 7 < 22, subtract 7 from both sides to get 3x < 15, then divide by 3 to find x < 5.

Front

What is the solution to the inequality -3x ≤ 18?

Back

To solve -3x ≤ 18, divide both sides by -3 (remember to flip the inequality sign) to get x ≥ -6.

Front

How do you graph the inequality x > 6?

Back

To graph x > 6, draw a number line, place an open circle at 6, and shade to the right to indicate all numbers greater than 6.

Front

What is the solution to the inequality 2x > 12?

Back

To solve 2x > 12, divide both sides by 2 to find x > 6.

Front

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

Back

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

Front

How do you represent the solution set of an inequality on a number line?

Back

The solution set of an inequality is represented on a number line by using open or closed circles at the endpoints and shading the appropriate direction.