To solve the inequality abs(x-4)<3, we first need to graph each side of the inequality in our calculators. abs(x-4)<y y<3 Then we will find any critical points of the inequality by finding the points of intersection between these two graphs. x=1 x=7 Since x=1 and x=7 are both critical values of the inequality, we need to pick three test points - one to the left of x=1, one to the right of x=7, and one in-between x=1 and x=7. The test point(s) that gives a "true" statement when we plug in to the inequality is the correct side to shade on.