 I'd like to just go through a couple absolute value inequality examples just to show you how you could solve each of these by hand. So if you remember from class with absolute values you always have to compare your inequality to both the positive value, so in this case one, and the negative value. But when you're comparing it to the negative value you need to flip the inequality sign. So the two inequalities we would be solving are 3x-1 is less than 1, 3x-1 is greater than negative 1. And to solve we add 1 to each side, divide by 3, x is less than two thirds, is one of our solutions, and then here if we add 1, divide by 3 we get x is greater than zero. So what we need is we need x to be less than two thirds and we need x to be greater than zero. So less than two thirds would be to the left here, and greater than zero would be to the right. And so the solution is right here where the two overlap and that solution is going to be the interval parenthesis zero to two thirds. So just remember when you're solving the inequality over here to flip the negative sign. If you think about what your graph would look like for an inequality remember it's always a v. So if I were to draw that graph in down here notice here I want it to be less than one. So less than is anywhere where it is below this x-axis here or the line one. And less than would be the bottom of the v wherever it is below the line which again is from zero to two thirds. So you can think about it in terms of the graph or you can think about it by solving it by hand. Let's look at one more example that is a little bit trickier. With this example the main thing that you want to remember is you cannot split up your inequality into the two values, the positive and the negative until the absolute value is by itself. So first here I'll subtract 12 and then I have to get rid of this negative sign in front of the absolute value. I can't distribute it and so I would end with the absolute value of 9-x is not less than since I divided by a negative one I'm going to flip it and make it greater than 13. And so at this point once the absolute value is by itself then I can solve my two inequalities. One inequality stays exactly the same while the second we have to flip the inequality sign and flip the sign of what we're solving for. So 9-x is greater than 13, 9-x is less than a negative 13. Okay now I will re-solve those or rewrite those up here at the top. 9-x is greater than 13 or 9-x is less than negative 13. When you're solving this the one thing just to be aware of is that we have a negative x. So again we have to divide by a negative one and when we divide by a negative one we flip the sign again. So x has to be less than negative four or if we solve over here we again divide by a negative one and so we flip the sign and x has to be greater than 22. So on the number line less than negative four is to the left greater than 22 is to the right and so our solution is going to be written in two pieces. On the left the way that we would describe this piece would be negative infinity to negative four all with parentheses and on the right this would be described as 22 to infinity. Again if you think of what your graph looks like here for it to draw this v in okay we want the part of the graph where it is greater than because notice what we ended with before was that we wanted it to be greater than 13 so the part above the graph and this is the section above the graph and this is the section above 13 so it's our two ends to the graph.