When solving this inequality, the first thing we need to do is get the absolute value all by itself on one side. So we're going to subtract the two before we even deal with the absolute value. It has to be on one side by itself. Subtract 2 from each side, so we get the absolute value of X -, 2 grade or. Then seven 9 -, 2 is 7. Now, this is an OR statement grade or. If it had been a less than, it was an AND statement. If it's an OR statement, it means anywhere that it's shaded in the first inequality or in the second inequality. If it's an AND statement, it has to be where they're both shaded. So our definition of absolute value is that the inside of an absolute value can be positive or the inside of an absolute value can be negative. So that inside piece X -, 2 is going to be greater than 7 or the opposite or the negative of the inside piece negative of the X -, 2 is greater than 7. Now to get rid of that negative, we could divide the whole thing through by a -1. And that's what most textbooks show is they show that second line of the X -, 2 less than -7. But the reason that that works comes from the official definition of absolute value, which says the inside of an absolute value is positive and the inside of an absolute value is negative. So now if we solve each of those inequalities, we get X greater than 9 or X less than -5. When we graph these on a number line, we're going to use an open dot or a parenthesis at -5. And also at 9:00, because I want X less than -5, I'm shading to the left. So open dot or parenthesis at -5 shaded to the left. When X is greater than nine, I'm having an open dot or a parenthesis at 9, and I'm shading off to the right. Now, when we write our final solution, we have to read the number line from left to right. So where does it start being true? It starts being true at negative Infinity. Where does it stop being shaded at -5 but there's a second place that it's also shaded. Hence we need to use our union symbol. When we have more than one place where it's shaded, we're always going to use the union. So then we have union starting again at 9 and going off to the right, out to Infinity.