LINEAR FUNCTIONS Solving Linear Inequalities (Page 2 of 4)

We now interpret the inequality 3x+4-(1/3)(x-2) > 0 in terms of the function that is graphed. The solution set will be all values of x for which the function Y1 has positive y-values. Let's use TRACE to identify where these values of x are. Since the x-intercept has a y-value of 0, the x-values we want must be either to the left or to the right of the intercept.

 TRACE key. Left arrow key....

 Right arrow key....

 Calculator screen image. Calculator screen image.

The x-values to the left of -1.75 yield negative y-values, those to the right yield positive y-values. The inequality
 3x+4-(1/3)(x-2) > 0 means that the graph of Y1 (the line) must lie above the x-axis. Looking at the graph, we see this is true if x is to the right of -1.75. So, the solution set is {x: x > -1.75}, or in interval notation, (-1.75, infinity).
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