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Linear and Compound Inequalities

A series of free Intermediate Algebra Video Lessons from Brightstorm online Algebra series.

Solving Linear Inequalities
If we want to solve for or describe a region in a coordinate plane, we can use linear inequalities. Linear inequalities give us a set of solutions as opposed to just one solution. Solving linear inequalities uses similar methods as solving multi-step equations, except that there are extra rules when using multiplication and division. We graph linear inequalities by shading regions of number lines or coordinate planes.

Set Operation: Union
A set operation is the collection of two data sets. Two data sets can be added together, which is called a union set operation. For example, the union of data set A with the data set B (A U B) is the set of all things which are members of either A or B. Set operations include union, intersections and complements.

Set Operations Intersection
A set operation is the collection of two data sets. Types of set operations include union, intersections and complements. Intersection set operations is a new set of data that is constructed by determining the values that two sets have in common. For example, the intersection of data set A and data set B is the set of all things which members of both A and B.

Solving a Three-part Linear Inequality - Compound Inequality
In mathematics, it can be useful limit the solution or even have multiple solutions for an inequality. For this we use a compound inequality, inequalities with multiple inequality signs. When solving compound inequalities, we use some of the same methods used in solving multi-step inequalities. The solutions to compound inequalities can be graphed on a number line, and can be expressed as intervals.

Applied Linear Inequalities : Linear Inequalities Word Problems
In Algebra II, we are sometimes asked to use linear inequalities to solve word problems. Solving linear inequalities word problems is very similar to solving word problems with linear equations. With word problems, we extract the relevant information and then set up a linear inequality to solve it.

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