Linear Inequalities

(1) Linear Inequality WORKSHEETS

(2) Linear Inequality Tutorial with Video Examples

(3) Systems of Linear Inequalities WIth Video Examples

(4) Other Youtube videos on Linear Inequalities

When graphing linear inequalities it is important to first graph the line as if it was an equation. For example:

If the problem was y > 2x + 3 then you would graph y = 2x + 3. There are various ways to graph lines. Here are some examples:

http://www.purplemath.com/modules/strtlneq.htm
http://www.coolmath.com/algebra/Algebra1/06Lines/04_intercepts.htm

Before you actually graph the line it is important to look at the inequality sign. There are two possiblities:

1) Less than (<) or greater than (>). In this case you the graph of the line needs to be dotted.

2) Less than or equal to and greater than or equal to. In this case the graph of the line needs to be solid.

After you have graphed the line (dotted or solid) it is then important to shade one side of the line. This is done because on one side of the line all the points make the inequality true and on the other side all the points make the inequality false. The solution to the inequality is all the points that make it true.

To do this you must test a point. If that point makes the inequality true, all the points on that side of the line are true. If it make the inequality false, then all the points on the other side of the line are true.

Procedure

1) Pick a point NOT on the line ( (0,0) is a good choice if possible).

2) Substitute the point in for the original inequality. Evaluate if it is a solution or not.

3) If it is a solution shade in the side the point is on. If it is NOT a solution then shade in the other side.

Above we learned how to graph the solution of a linear inequality. Now we move onto problems involving more than one inequality. Particularly we are going to look at systems of two inequalities.

The solution to a single linear inequality is all the ordered pairs (x, y) that make the inequality true. It is usually designated by a shaded region on a graph.

For a system of linear inequalities you are looking for all the points that make both inequalities true. This is done by graphing both inequalities and then looking to see where the shaded regions overlap. The overlap is the solution to the system. The procedure for solving these problems is:

1) Graph the first linear inequality. Shade the answer lightly using a horizontal pencil stroke.

2) Graph the second linear inequality. Shade the answer lightly using a vertical pencil stroke.

3) Identify the region where the two solutions overlap. Shade this region in darkly and then indicate it as the solution of the system.