Math Section 10 - Inequalities

In this set of Math Tutorials we cover Inequalities in details with clear guides, Inequalities formulas and working examples. Each tutorial includes example questions, a revision guide and supporting Inequalities calculators

We also provide online Inequalities Calculators which allow you to calculate specific Inequalities formula in support of the tutorials or to check and verify your own calculations in support of your Inequalities homework, math coursework or to help you improve your own understanding so it is easier to teach your children Inequalities.

Inequalities Learning Material and Inequalities Study Aide
Tutorial IDTitleTutorialVideo
10.1Solving Linear Inequalities
10.2Quadratic Inequalities
10.3Graphing Inequalities
10.4Systems of Inequalities

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Inequalities Tutorials Snapshot

This chapter deals entirely with inequalities - the complementary version of equations we discussed in the previous chapter on equations. The first tutorial begins with the definition of inequalities and their difference with equations illustrated with their simplest version - the first-order inequalities with one variable. Moreover, the symbols used to express the relationship between the two parts of a mathematical sentence representing an inequality are explained in detail. Solving inequalities of various types is the main focus of this tutorial through. Other things such as double inequalities, transformations allowed in inequalities, intervals and segments, linear inequalities in two variables and checking whether a number pair is a solution for a linear inequality in two variables or not, complete the framework of this long but key tutorial that is very useful in understanding how inequalities work.

The second tutorial of this chapter deals with quadratic inequalities, as an extension of the concept of quadratic equations. The first thing you will learn in this tutorial is how to identify whether a given number is a root of a quadratic inequality or not. Other things discussed in this tutorial include writing a quadratic inequality in the standard form, studying the sign and finding the solution set of a quadratic inequality. Perhaps the most important thing discussed in this tutorial is, however, the study of the inequalities sign based on the roots of the corresponding quadratic equation and more specifically, on the sign of the discriminant.

The third tutorial of this chapter deals with the graphs of inequalities. The most important thing you will learn in this tutorial (but not only) is the shape and orientation of linear and quadratic graphs based on the signs and values of the coefficients a and b and the constant c. Other things you will learn in this tutorial include finding the standard form of a linear inequality when its graph is given and identifying the direction of the solution set in linear and quadratic inequalities. All concepts and methods explained in this tutorial are illustrated with examples for a better understanding.

The fourth tutorial deals with systems of inequalities. Obviously, the only method available here is the graphing method, as the rest of the methods would require lots of effort in identifying the solution set because of the different signs used in inequalities. In this tutorial, you will learn the answers to questions like, how to identify the solution set (zone) of a system of linear inequalities; how to find the minimum/maximum value of the solution set in systems of inequalities; how to find the leftmost/rightmost value of the solution set in systems of inequalities; how to solve systems of three linear inequalities; how to solve systems of inequalities where at least one inequality is not linear, and so on.

Inequalities Calculators

The following Math Calculators are provided in support of the Inequalities tutorials.