Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.9 Graph and Solve Quadratic Inequalities - 4.9 Exercises - Skill Practice - Page 305: 51


$$x\leq -1.5 \\ x\geq 3.5$$

Work Step by Step

In order to solve this problem, we first get rid of the inequality symbol and replace it with an equal sign. Next, we get zero on one side of the equation, and we solve the equation to find the critical values of the inequality. Doing this, we obtain: $$4x^2-8x-21 =0 \\ (2x+3)(2x-7) =0 \\ x=-1.5, 3.5$$ Now that we have found the critical values, we plug in values on either side of the critical values as well as in between them to find which values result in true statements. The values that result in true statements are in regions that are solutions to the inequality. Thus, we write the solution: $$x\leq -1.5 \\ x\geq 3.5$$
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