Stitz-Zeager_College_Algebra_e-book

Solve the inequality and express your answer in

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Unformatted text preview: he category x < −1, we keep them all. For the second case, we assume x ≥ −1. Our inequality becomes x + 1 ≥ x+4 , which gives 2x + 2 ≥ x + 4 or 2 x ≥ 2. Since all of these values of x are greater than or equal to −1, we accept all of these solutions as well. Our final answer is (−∞, −2] ∪ [2, ∞). y 4 3 2 −4 −3 −2 −1 1 2 3 4 x We now turn our attention to quadratic inequalities. In the last example of Section 2.3, we needed to determine the solution to x2 − x − 6 < 0. We will now re-visit this problem using some of the techniques developed in this section not only to reinforce our solution in Section 2.3, but to also help formulate a general analytic procedure for solving all quadratic inequalities. If we consider f (x) = x2 − x − 6 and g (x) = 0, then solving x2 − x − 6 < 0 corresponds graphically to finding the values of x for which the graph of y = f (x) = x2 − x − 6 (the parabola) is below the graph of y = g (x) = 0 (the x-axis.) We’ve provided the graph again for referenc...
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