 So let's solve the absolute value inequality, absolute value x minus 2 greater than 5. So we'll use the test point method and solve the corresponding E-Qualities. So to solve absolute value x minus 2 equals 5, we solve two equations, x minus 2 equals 5, and x minus 2 equals negative 5. Solving these two equations separately gives us... So we started out by solving an E-Quality, but like a good math student, or a good human being, we acknowledge the existence of the inequality, and we take steps to address it. Remember, we're actually trying to solve this inequality. Since the critical values solve the E-Quality absolute value x minus 2 equals 5, but the inequality is strict, the critical values are not included. And so our solution has critical values 7 and negative 3, which are not included. Let's go ahead and plot those. So since they are not included, we'll want to use the open circle, and so we'll put an open circle at negative 3 and at 7. Now notice that the critical values separate the number line into three parts. So we'll test a point in each region. In this leftmost region, we'll let x be a large negative number, and then x minus 2 is a large negative number. The absolute value of x minus 2 will be a large positive number, and since we want the inequality to be greater than 5, a large positive number will satisfy the inequality, and so we want to include the region to the left of negative 3. In the center, we'll use x equals 0 as our test value, so we'll take our inequality. Is it true that the absolute value of x minus 2 is greater than 5 when x is equal to 0? So we'll replace and simplify, and since this guy and his friends say it's true, it must be true. Well, let's think for ourselves for a moment, and in fact this statement is false, so we exclude the central region. In the right region, we'll let x be a large positive number, and then x minus 2 is a large positive number. The absolute value of x minus 2 is a large positive number, and again, since we want our absolute value to be greater than 5, this will satisfy the inequality, and so we include the region to the right of x equals 7. So let's graph our solution. We've already graphed the endpoints. We want the region to the left of negative 3, so we'll switch to our line tool and start at negative 3 and go left, and we also want the region to the right of 7. So again, using our line tool, we'll start at 7 and go to the right, and it's important to make sure that we've gone far enough to get the right or left pointing arrow, and we have so we can submit and get our score.