INSTRUCTOR: We're going to visualize the solutions to an absolute value inequality. In this case, my problem is 2 times the absolute value of x minus 8 plus 2 is greater than 9. And when you type that right in, it actually just gives you the solution set. 

So we can visualize the solution here. Really, we don't need x and y because it's just solutions in the form of x. So if we ignore the vertical component of it, we can see that below 4 and 1/2, it looks like, and above 11 and 1/2 will be the solutions for x. 

But this is actually not the best way to understand why that's the solution, so let's go back to center, clear it out, and start over. This time, I'm going to enter the left hand side of the inequality as a function, f of x equals 2 times the absolute value of x minus 8 plus 2. 

And there, we can see the actual behavior of the left hand side of the inequality. And it's typed in function notation, so it gives us a little bit more use for it. And again, it might be good to put that in the middle of the screen. 

Now, the inequality was when that function or the left hand side is greater than 9. So let's see where those intersect. f of x can be replaced with y and is being interpreted as y, so we're just setting y equals to 9. And now, I'm going to put the full inequality back in. This time, I'll use that f of x that I already defined. So you can see, everything meets up perfectly. 

Let's go through what's going on here. The left hand side of the inequality has a behavior of a V shape. We want to know when that's above 9, so we want to know when the black lines are above the red line. 

That's going to happen when we're to the left of 4.5 or to the right of 11.5. Now, if I want to share this graph, I'll click the Share button, copy the link, and paste it in the comments of the submission.