Graphing and Writing Inequalities - Overview
Solve Absolute Value Inequalities - Example 1
Solve Absolute Value Inequalities - Example 2
Solve Absolute Value Inequalities - Example 3
Solve Absolute Value Inequalities - Example 4
Syracuse University
Graphing and Writing Inequalities - Example 4


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So in this example, we're being asked to write it inequality to represent the following freezes. They tell us to let X represent the number, and then we're gonna graft a solution set on the number line. So let's start with number one. It says a number is greater than or equal to three. Well, remember, when they say a number, we're going to be using acts our inequality sign is represented by the phrase is greater than or equal to. So that means we need to use a greater than or equal to sign. I mean, put that mark a little better. There we go. And the last thing is, Well, what is it greater than or equal to? Well, it's greater than or equal to three. So now we'll have our inequality. X is greater than or equal to three. Now we're being asked to graft the solution set on the number line. So remember we first have to determine should be used open or close circle at three. Well, because it says greater than or equal to three. That means three Issa solution. So at three, we're going to use a closed circle. Then once you put your circle on your number line. Now we have to determine. Should we shade to the left or to the right of three? Well, where are the values of X that are greater than or equal to three? Well, that would be to the right of three, like 456 etcetera. So we're going to shade to the right of three. So now we have graft. Our solution set on our number line. Now let's take a look at number two. It says that negative one is less than a number. So again, let's go through and pick out the key points. So were first, starting with that. The number is negative one, so that will start. Next is our phrase to represent our inequality sign. It says it's less than well, what is it less than? Well, it says a number which remember, were referring to a Zac's. So now we have written inequality to represent our freeze. Negative one is less the next, So now what we need to do is graft. The solution set on the number line. So again, the first thing we need to determine it should be using open circle or a close circle at negative one. Well, is negative. One of solution? No, it is not. Therefore, we're going to use an open circle now. We have to determine should be shade to the left it to the right. We'll notice in our inequality sign that are variables written second, which remember, it could be a little bit tricky. So what we're gonna do is we're gonna flip it around. X is going to go first. Negative one is going to go second and know this how in our inequality symbol that if you almost think of it as an animal, the mouth is open toe X. So when we flip it around, it should still be open toe X. So when we do this, what that means is that X should be greater than negative one. Okay, Now that we know X has to be greater than negative one, this makes it a little bit easier for us to determine our shading. So where the values of X that are greater than negative one? Well, that would be to the right of negative one on our number one, which tells us when we go ahead and do our shading, we're going to shade all the values of X that are greater than negative one number words. We're going to shade to the right of negative one on our number line. So now we have written inequality and grafted solution set on a number line.

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