Lesson All About Graphing Inequalities

One concept in algebra that a lot of people have trouble with is graphing inequalities. An inequality is basically an equation with the equal sign removed and replaced by < or >, or the variation of those which include half an equal sign under it. Truth is, if you can graph a line, you can graph an inequality. It's very simple:

---Suppose you have the inequality .

Just graph the line for y=x+3, for a start. Once you've done that, just simply shade the part of the graph ABOVE that line to show that y is more than that. But there is one more step. Dot the line. Make sure it is dotted, because that shows that y does not include that line, y is above that line and ONLY above that line.
Now if , you would just draw the line normally and shade. No dots.

---Suppose the inequality was .

Again, graph the line for y=x+3. Then dot it, then shade UNDER it this time to show that y is less than that. Again, if , then you would just draw the line normally and shade. No dots.

---Now you've heard me say above and under the line, but what about if it were a vertical line, such as ?

Graph the line for x=4. Then dot the line and shade TO THE RIGHT of the line, since x values get higher going right on the x axis. Again, if it were , then, just draw the line normally and shade. No dots.

---What about ?

Again, draw the line for x=4, dot it, and shade TO THE LEFT of the line. If it were , then again, just draw the line normally and shade. No dots.

That's the end of this lesson. I hope this explanation made graphing inequalities much easier for you!