Inequalities
Solve and graph inequalities
lessons (7)
Introduction to Inequalities
Learn the basics of inequalities and how to compare values using inequality symbols.
Solving and Graphing Inequalities
Learn how to solve one-step and two-step inequalities and represent solutions on a number line.
Graphing Inequalities on a Number Line
Learn how to represent inequalities visually using open circles, closed circles, and shading on a number line.
One-Step Inequalities
Learn to solve inequalities that require just one operation, and understand why the inequality sign flips when multiplying or dividing by a negative.
Two-Step Inequalities
Learn to solve inequalities that require two operations, combining addition/subtraction with multiplication/division.
Compound Inequalities
Learn to solve and graph compound inequalities using AND and OR connectors.
Absolute Value Inequalities
Learn to solve inequalities involving absolute value by understanding distance from zero.
Inequalities extend equation-solving skills to describe relationships where quantities are not equal but greater or less than each other. In real life, we often deal with ranges and constraints rather than exact values—budgets, speed limits, and safety margins all involve inequalities. Understanding inequalities is essential for optimization and real-world problem solving.
In this topic, you will learn to solve one-step and multi-step inequalities using techniques similar to equation solving. You will discover the critical rule about inequality direction when multiplying or dividing by negative numbers. Graphing solutions on number lines and using interval notation will help you visualize and communicate solution sets.
Our lessons connect inequalities to practical scenarios: setting budgets, determining eligibility, and defining acceptable ranges. With compound inequalities and absolute value inequalities, you will tackle increasingly sophisticated problems that model real constraints and conditions.
What Students Will Learn
- Solve one-step and two-step inequalities
- Apply the rule for multiplying/dividing by negatives
- Graph inequality solutions on a number line
- Write solutions using interval notation
- Solve and graph compound inequalities (and/or)
- Solve absolute value inequalities
- Translate real-world constraints into inequalities
Frequently Asked Questions
Why does the inequality sign flip when multiplying by a negative?
Multiplying by a negative reverses the order of numbers. For example, 2 < 5, but -2 > -5. The inequality must flip to maintain the correct relationship between the values.
What is the difference between < and ≤?
The symbol < means strictly less than (not including the endpoint), while ≤ means less than or equal to (including the endpoint). On a number line, < uses an open circle, ≤ uses a closed circle.
How are compound inequalities different?
Compound inequalities combine two inequalities. 'And' means both must be true (the intersection), while 'or' means at least one must be true (the union). They describe more complex ranges of solutions.