Inequalities

What is Inequalities?

Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Inequalities. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.

Check that you can explain Inequalities in your own words and give one example from everyday life. If you can do that, you have understood the core idea.

Understanding Inequalities gives you a reliable method you will reuse in later maths units, in science lessons and in data work.

Inequalities in detail

An inequality compares quantities that are not equal, using symbols such as < (less than), > (greater than), ≤ and ≥. The solution is usually a range of values, for example x > 3. You solve linear inequalities like equations, with one crucial exception: if you multiply or divide by a negative number, you must reverse the inequality sign.

Solutions can be shown on a number line, using an open circle for < and > and a filled circle for ≤ and ≥. Inequalities describe limits and constraints in real situations, such as a maximum budget or a minimum pass mark, and graphs of them shade regions of a plane.

How the interactive helps you understand Inequalities

Move the slope and y-intercept sliders. The line and its equation update, so you can see how the slope sets the steepness and the intercept sets where the line crosses the y-axis.

Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Inequalities.

Real-life uses and examples

• Use Inequalities when comparing prices, discounts or recipe quantities in everyday life.
• Explain Inequalities to a friend with a simple picture, such as a row of tiles or a bag of sweets.
• Spot Inequalities in exam questions, where it often sits inside a short word problem.

Common mistakes to avoid

• Forgetting units, signs or brackets when you apply Inequalities.
• Memorising the steps for Inequalities without checking why they work.
• Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.