To solve the inequality x^2-5>x+1, we first need to graph each side of the inequality in our calculators. y<x^2-5 y>x+1 Then we will find any critical points of the inequality by finding the points of intersection between these two graphs. x=-2 x=3 Since x=-2 and x=3 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=3, and one in-between x=-2 and x=3. The test point(s) that gives a "true" statement when we plug in to the inequality is the correct side to shade on.