10.7 Exercises Do the exercises, and check your work. 1) When solving a quadratic inequality, how do you know when to include and when to exclude the endpoints in the solution set? 2) If a rational inequality contains a or symbol, will the endpoints of the solution set always be included? Explain your answer. Objective 1: Solve a Quadratic Inequality by Graphing For Exercises 3–6, use the graph of the function to solve each inequality. 3) y x2 4x 5 4) y x2 6x 8 Objective 2: Solve a Quadratic Inequality Using Test Points Solve each quadratic inequality. Graph the solution set, and write the solution in interval notation. 7) x2 6x 7 0 8) m2 2m 24 0 9) c2 5c 36 10) t 2 36 15t 11) 3z2 14z 24 0 12) 5k2 36k 7 0 13) 7p2 4 12p 14) 4w2 19w 30 15) b2 9b 0 16) c2 12c 0 17) m2 64 0 18) p2 144 0 19) 121 h2 0 20) 1 d 2 0 Objective 3: Solve Quadratic Inequalities with Special Solutions Solve each inequality. 21) (h 5)2 2 22) (3v 11)2 20 23) (2y 1)2 8 24) (r 4)2 3 25) (4d 3)2 1 26) (5s 2)2 9 Objective 4: Solve an Inequality of Higher Degree Solve each inequality. Graph the solution set, and write the solution in interval notation. 27) (r 2)(r 5)(r 1) 0 28) (b 2)(b 3)(b 12) 0 29) (6c 1)(c 7)(4c 3) 0 30) (t 2)(4t 7)(5t 1) 0 Objective 5: Solve a Rational Inequality Solve each rational inequality. Graph the solution set, and write the solution in interval notation. 31) 7 p 6 0 32) 3 v 2 0 33) 5 z 3 0 34) 9 m 4 0 35) x 4 x 3 0 36) a 2 a 1 0 x y 1 x 1 y 5 a) x2 4x 5 0 b) x2 4x 5 0 a) x2 6x 8 0 b) x2 6x 8 0 5) y 1 2 x2 x 3 2 6) y x2 8x 12 x y 5 5 5 5 x y 5 2 5 a) 1 2 x2 x 3 2 0 b) 1 2 x2 x 3 2 a) x2 8x 12 0 b) x2 8x 12 0 0 www.mhhe.com/messersmith SECTION 10.7 Quadratic and Rational Inequalities 689
messersmith_power_intermediate_algebra_1e_ch4_7_10
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