Graphing Inequalities

Graphing inequalities. (If you don’t know how to solve inequalities check under elementary algebra.)

First you need to solve the inequality. Solve for Y. (E.g. 2x – 3y < 6)

2x – 3y < 6

–3y < –2x + 6

y > ( 2/3 )x – 2

• • Remember the inequality sign must be flipped if you multiply or divide by a negative number. (notice how it is flipped at the end of the example)

After you solve for y the equation needs to be graphed.

The type of line matters when graphing. A dashed line stands for a less than or a greater than. It is similar to an open dot on a number line. A solid line stands for a less than or equal to or an greater than or equal to.  The solid line is similar to a closed dot on the number line.

Next the graph needs to be shaded in according to the inequality sign.

 If it is greater than, or greater than or equal to, the space above the line or to the right of the line, depending on the slope of the line, needs to be shaded in.

If the inequality being graphed is less than, or less than or equal to, the space below the line or to the left of the line, depending on how the line is situated, needs to be graphed.

If you are graphing a system of inequalities similar steps are taken

• • First solve for Y.

  • Graph the first line according to the inequality (solid or dashed)

  • Next depending on if it is a less than or a greater than you should prepared to shade it in (but wait until you graph the other lines in the system). For now just put arrows on the top or bottom of the line to show which side needs to be graphed.

  • After all inequalities are solved for, graphed (solid or dashed), marked with arrows so that you remember where to shade, then you can actually shade the area where all of the inequalities overlap.

How to Graph a Linear Inequality

First, graph the "equals" line, then shade in the correct area.

There are three steps:

• • Rearrange the equation so "y" is on the left and everything else on the right.

  • Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

  • Shade above the line for a "greater than" (y> or y≥)

  • or below the line for a "less than" (y< or y≤).

Let us try some examples:

Example: y≤2x-1

1. The inequality already has "y" on the left and everything else on the right, so no need to rearrange

2. Plot y=2x-1 (as a solid line because y≤ includes equal to)

3. Shade the area below (because y is less than or equal to)

Here is a good page to take a glance at. It gives an example of how to solve a system of inequalities and it walks you through it step by step. http://www.purplemath.com/modules/syslneq.htm