 So once you have equations, you have inequalities. So far, we've solved linear inequalities by finding critical points and evaluating test points. We solved quadratic inequalities by finding critical points and evaluating test points. We solved root inequalities by finding critical points and evaluating test points. We solved rational inequalities by finding critical points and evaluating test points. This suggests that we'll solve absolute value inequalities in the same way, and in fact we will. At least for now. Because of the geometric meaning of absolute value, we have another way of solving them. So let's start off by solving this absolute value inequality in exactly the same way we've solved all other inequalities. First we'll solve our absolute value equation, and so that's 8x minus 5 equals 3, or 8x minus 5 equals negative 3, solving that gives us our critical values. Again, like a good human being or a good math student, we recognize the inequality. So let's graph our inequality. Since the inequality allows for equality and the critical values solve the equation, then we can include the critical values in our solution. And now we'll test a point in each of the three intervals. In the first interval we'll test x equals 0, and this is true, so we'll include this first interval. Now we have this middle interval, and we have to check something in this interval, how about 3 fourths, and our inequality is false, so we have to exclude this interval. And finally in our last interval we can test x equals 1 million, and this is true, so we should include this interval. So here's our graphical solution. We can rewrite our solution in interval notation.