When we solve an equation
and come up with a solution
, 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
to an inequality. Let’s go back and look at the inequality
. To show that all values greater than -1 are part of the solution, we can draw a number line
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
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
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
So far we’ve see that symbols of < and > mean
you have an open circle
and symbols of
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