Recall that coordinate plane is divided into four equal quarters called quadrants. The first quadrant is the one where x and y are positive, and the rest are labeled counterclockwise. Recall that we need our inequality's solution set to lie only in the first and fourth quadrants.
Since we are going to work with an absolute value inequality, we can start by reviewing the parent function for the absolute value function. This is y=|x|, which is V shaped.
We need a way to transform this vertical V-shaped graph into an horizontal one. That way, it would be limited to the required quadrants. Instead of y=|x| we can use the relation x=|y|. We would graph it the same way as y=|x|, but now the positive x-axis will play the role the positive y-axis played in y= |x|.
Notice that this is not a function, since there are x values paired with more than one y value. We need the solution set to lie on the right of our graph. Therefore, we can use a test point in this region to see what inequality symbol would give us a true statement. For example, let's use the test point (1,0).
