To solve the inequality abs(x-3)<=(1/2)x, we first need to graph each side of the inequality in our calculators. y>=abs(x-3) y<=(1/2)x Then we will find any critical points of the inequality by finding the points of intersection between these two graphs. x=2 x=6 Since x=2 and x=6 are both critical values of the inequality, we need to pick three test points - one to the left of x=2, one to the right of x=6, and one in-between x=2 and x=6. The test point(s) that gives a "true" statement when we plug in to the inequality is the correct side to shade on.