# Linear and Compound Inequalities

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A series of free, online Intermediate Algebra Lessons or Algebra II lessons.

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In this lesson, we will

- review how to solve linear inequalities
- learn the set operation called union
- learn the set operation called intersection
- review how to solve or graph compound inequalities
- learn how to solve linear inequalities word problems

### Review 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.

Linear Inequalities

Solving and Graphing Inequalities using Addition or Subtraction

Solving and Graphing Inequalities using Multiplication or Division

Solving and Graphing Multistep Inequalities

Graphing Inequalities with Two Variables

### 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.

How to define union.

### Set Operation: 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.

How to define intersection.

### Solving a Three-part Linear Inequality
- Compound Inequality

In mathematics, it can be useful to limit the solution or even have multiple solutions for an inequality. For this we use a compound inequality, which consists of 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.

Review Solving and Graphing Compound Inequalities

### 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.

How to find a test score to keep the class grade at least 90%.

Solving Word Problems Involving Inequalities - Example 1

Solving Word Problems Involving Inequalities - Example 2

Solving Word Problems Involving Inequalities - Example 3

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