ABSOLUTE VALUE FUNCTIONS Solving Inequalities (Page 2 of 2)

We now interpret the inequality abs(2x+1) > 8 in terms of the two functions we have graphed. The solution set will be all values of x for which the absolute value function Y1 has y-values greater than those of the constant function Y2. Let's use TRACE to identify where these values of x are. Since the y-values of the two functions are equal at the intersection points, the x-values we want must be either to the left or to the right of these points. Use the up or down arrow keys to move back and forth between the graphs and compare the y-values at several places.

 TRACE key.
 Left arrow key.... Up arrow key. or Down arrow key.
 Right arrow key.... Up arrow key. or Down arrow key.		 Calculator screen image. Calculator screen image. Calculator screen image.

The inequality abs(2x+1) > 8 means that the graph of Y1 must lie above the graph of Y2. Looking at the graphs, we see this is true if x is to the left of the first intersection point x = -4.5 or to the right of the second intersection point x = 3.5. So, the solution set is {x: x < -4.5 or x > 3.5}, or in interval notation, (-infinity, -4.5)U(3.5, infinity).
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