Solving and Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

Front

What are the different types of inequalities?

Back

The different types of inequalities include linear inequalities, polynomial inequalities, rational inequalities, and absolute value inequalities.

Front

How do you graph an inequality on a number line?

Back

To graph an inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate region.

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

When solving inequalities, when do you flip the inequality symbol?

Back

You flip the inequality symbol when you multiply or divide both sides of the inequality by a negative number.

Front

What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more inequalities, often connected by 'and' or 'or'.

Front

How do you solve a compound inequality?

Back

To solve a compound inequality, solve each inequality separately and then combine the solutions, considering the type of compound inequality.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

What is interval notation?

Back

Interval notation is a way of writing the solution set of an inequality using intervals, such as (a, b) or [a, b].