Exercise 32 Page 271

To graph the given inequality, we will begin by graphing the boundary line, $y=3x-2.$ Note that since the inequality is not strict, the boundary line will be solid.

Let's now use $(0,0)$ as a test point to check whether the shaded half-plane is correct. Since the test point did not produce a true statement, we will shade the region that does not contain $(0,0).$

The error was shading the incorrect half-plane.