When we solve an

equation and come up with a

solution such as

, that means that 4 is the only value that makes that

equation true. But when solving inequalities, we get an answer that is also in the form on an inequality

. This means that any value of x that is greater than -1 will make the

inequality true. In other words, there are infinitely many values that will work. If you want to see how linear inequalities are solved,

click here.

This lesson will focus on how to

graph the

solution to an inequality. Let’s go back and look at the

inequality mentioned above,

. To show that all values greater than -1 are part of the solution, we can draw a

number line and

graph the solution. Let’s start by drawing a blank number line. It can be as long or as short as you like as long as it shows the

solution completely.

Now we need to draw our

solution on the number line.

Since -1 is not included in the solution, we do not fill in the circle. Whenever the

inequality is < or > there will be an open

circle on the number line. Since every number larger than -1 is included, we want to shade that portion of the number line.

If we had an

inequality like

we would shade the

circle at 2 and shade the

number line to the left of 2. (

**L**ess than means we shade to the

**L**eft.)

So far we’ve see that symbols of < and >

mean you have an open

circle and symbols of

and

you have filled in circle. When > and

are used, you shade to the right. And when < and

are used, you shade to the left.

We can use these same rules for double inequalities. Remember that a double

inequality “sandwiches” the

variable between two values, like

. This means any values of x between -1 and 3 are part of our solution. In this case, our

number line graph will not have an end portion shaded, but rather just be shaded between -1 and 3.

It is possible for the two inequalities in a double

inequality to be different. In other words, one

side may have a filled in

circle yet the other

side can be an open circle. Look at the

graph for