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How Do You Graph an Inequality on a Number Line?Graphing x = a
Before we graph an inequality on a number line, let's look at how to graph an expression with an equals sign. If you had to graph x = 2, that means that x must be exactly equal to 2. It cannot be any other number except for 2. To graph this on a number line, you simply put a dot at 2 to show that there is only possible solution. Graphing x > a Now let's look at what happens to the graph if we change it to x > 2. This means that x must be greater than or equal to 2. When x is just equal to 2, 2 is the only possible solution. When the symbol is changed to >, it now includes solutions that are larger than 2. To graph all of these possible solutions, we put a solid point at 2 (to show that 2 is included as a solution) and draw a ray towards all the numbers larger than 2 (to the right). The point is shaded in at 2 because 2 is included as one of the solutions. All of the numbers to the right of 2 on the number line are also included because they are greater than 2. Graphing x > a
What happens if we remove the line under the inequality and change it to x > 2. This means x must be strictly greater than 2. Now 2 is no longer a solution because 2 is not greater than itself. But 2.1 is still a solution and so is 2.000001. How do you show that exactly 2 does not count but 2.000001 counts? You draw an open circle at 2. An open circle indicates that the number is not a solution. 2 does not count, but anything to the right of it on the number line is a solution. Graphing x < a If we switch the sign around to x < 2, it becomes x is less than 2. We will still use an open circle to show that 2 is not a solution (2 is not less than itself). This time, we need to draw the ray to the left to indicate that all the numbers smaller than 2 are solutions to the inequality. Graphing x < a
If we add the line back in under the inequality symbol, it becomes less than or equal to. To graph x < 2, we change the point to a solid circle to show that 2 is now included as a solution. Then draw a ray to the left to show that all the numbers 2 or less are solutions to the inequality. Powered by Interact 
