Linear Inequalities

Topics for Today:

We are still finding our way around the coordinate plane, and today we discussed how to graph the solution to a linear inequality.  A linear inequality describes a region of the coordinate plane that has a boundary line.  The solution to a linear inequality are all the coordinate points that make a linear inequality true.  The solutions to inequalities contain infinitely many more solutions than that of equations, and the same is true for linear inequalities.

Solutions to linear inequalities involve graphs.  The process for graphing linear inequalities is very similar to graphing linear equations with a few additional details.  The basic process for graphing linear inequalities is

1. Treat the inequality just like an equation.  Use the equation to graph the boundary line.
2. Determine if the boundary line is a part of the solution
• For equations that are strictly greater or less than (>  or <), the boundary is NOT included and should therefore be a dashed line.
• For equations that are greater than or equal to or less than or equal to (≥ or ≤) the boundary line IS included and should therefore be drawn as a solid line.  
3. Next, determine which side of the line the solution points fall.  The best way to accomplish this is to pick a point on either side, and test the inequality for truth.  The point that generates a true statement is on the side of the line with the solution.
4. Once the correct side of the boundary is found, shade this region to indicate where the solutions are.  

Vocabulary: linear inequality, solution of an inequality

Sections Covered in Textbook:

7-5: Linear Inequalities (pages 370-375)

Resources & Tutorials:

1. What is a linear inequality?
2. How do you figure out if the boundary is part of the graph of the inequality?