Explanation Given information: Given inequality is | x − 1 x + 2 | ≥ 2 Calculation: The absolute value inequality | x | ≥ a can be written as x ≤ − a or x ≥ a The inequality can be written as: x − 1 x + 2 ≤ − 2 or x − 1 x + 2 ≥ 2 Consider x − 1 x + 2 ≤ − 2 x − 1 x + 2 + 2 ≤ − 2 + 2 x − 1 x + 2 + 2 ( x + 2 ) x + 2 ≤ 0 x − 1 x + 2 + 2 x + 4 x + 2 ≤ 0 x − 1 + 2 x + 4 x + 2 ≤ 0 3 x + 3 x + 2 ≤ 0 3 ( x + 1 ) x + 2 ≤ 0 x + 1 x + 2 ≤ 0 To solve an inequality with exponents or in rational form, the factors of the inequality are considered. Here the expression is already completely factored. Here, the solutions for the factors x + 1 = 0 and x + 2 = 0 are x = − 1 and x = − 2 respectively. But the expression is undefined at -2. Hence, the number line is divided into the intervals: ( − ∞ , − 2 ) , ( − 2 , − 1 ) and ( − 1 , ∞ ) Now a number from each interval is selected to check if it satisfies the inequality. Consider the number x = − 4 for the interval ( − ∞ , − 2 ) : Plugging the value in the interval, x + 1 x + 2 ≤ 0 − 4 + 1 − 4 + 2 ≤ 0 − 3 − 2 ≤ 0 3 2 ≤ 0 The statement is false. Hence, this interval does not satisfy the inequality. Consider the number x = − 1.5 for the interval ( − 2 , − 1 ) : Plugging the value in the interval, x + 1 x + 2 ≤ 0 − 1.5 + 1 − 1.5 + 2 ≤ 0 − 0.5 0.5 ≤ 0 − 1 ≤ 0 The statement is true. Hence, this interval satisfies the inequality. Consider the number x = 2 for the interval ( − 1 , ∞ ) : Plugging the value in the interval, x + 1 x + 2 ≤ 0 2 + 1 2 + 2 ≤ 0 3 4 ≤ 0 The statement is false. Hence, this interval does not satisfy the inequality. Hence, the solution for the inequality x − 1 x + 2 ≤ − 2 is ( − 2 , − 1 ] Consider x − 1 x + 2 ≥ 2 x − 1 x + 2 − 2 ≥ 2 − 2 x − 1 x + 2 − 2 ( x + 2 ) x + 2 ≥ 0 x − 1 x + 2 − 2 x + 4 x + 2 ≥ 0 x − 1 − 2 x − 4 x + 2 ≥ 0 − x − 5 x + 2 ≥ 0 To solve an inequality with exponents or in rational form, the factors of the inequality are considered

Precalculus: A Unit Circle Approach (3rd Edition)

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Author: J. S. Ratti, Marcus S. McWaters, Leslaw Skrzypek

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Chapter A.7, Problem 61E

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Chapter A.7, Problem 60E

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Chapter A.7 Solutions

Precalculus: A Unit Circle Approach (3rd Edition)

Ch. A.7 - In Exercises 7-12, solve each compound or...Ch. A.7 - In Exercises 7-12, solve each compound or...Ch. A.7 - In Exercises 13-18, solve each compound and...Ch. A.7 - In Exercises 13-18, solve each compound and...Ch. A.7 - In Exercises 13-18, solve each compound and...Ch. A.7 - In Exercises 13-18, solve each compound and...Ch. A.7 - In Exercises 13-18, solve each compound and...Ch. A.7 - In Exercises 13-18, solve each compound and...Ch. A.7 - In Exercises 19-24, solve each combined...Ch. A.7 - In Exercises 19-24, solve each combined...Ch. A.7 - In Exercises 19-24, solve each combined...Ch. A.7 - In Exercises 19-24, solve each combined...Ch. A.7 - In Exercises 19-24, solve each combined...Ch. A.7 - In Exercises 19-24, solve each combined...Ch. A.7 - Prob. 25E Ch. A.7 - Prob. 26E Ch. A.7 - Prob. 27E Ch. A.7 - Prob. 28E Ch. A.7 - Prob. 29E Ch. A.7 - Prob. 30E Ch. A.7 - In Exercises31-42, solve each inequality. Write...Ch. A.7 - In Exercises31-42, solve each inequality. Write...Ch. A.7 - Prob. 33E Ch. A.7 - In Exercises31-42, solve each inequality. Write...Ch. A.7 - In Exercises31-42, solve each inequality. Write...Ch. A.7 - Prob. 36E Ch. A.7 - In Exercises31-42, solve each inequality. Write...Ch. A.7 - Prob. 38E Ch. A.7 - In Exercises31-42, solve each inequality. Write...Ch. A.7 - In Exercises31-42, solve each inequality. Write...Ch. A.7 - Prob. 41E Ch. A.7 - Prob. 42E Ch. A.7 - Prob. 43E Ch. A.7 - Prob. 44E Ch. A.7 - Prob. 45E Ch. A.7 - Prob. 46E Ch. A.7 - Prob. 47E Ch. A.7 - Prob. 48E Ch. A.7 - Prob. 49E Ch. A.7 - Prob. 50E Ch. A.7 - Prob. 51E Ch. A.7 - Prob. 52E Ch. A.7 - Prob. 53E Ch. A.7 - Prob. 54E Ch. A.7 - Prob. 55E Ch. A.7 - Prob. 56E Ch. A.7 - Prob. 57E Ch. A.7 - Prob. 58E Ch. A.7 - Prob. 59E Ch. A.7 - Prob. 60E Ch. A.7 - Prob. 61E Ch. A.7 - Prob. 62E Ch. A.7 - Prob. 63E Ch. A.7 - In Exercises 53-66, Solve each inequality. 64....Ch. A.7 - Prob. 65E Ch. A.7 - Prob. 66E Ch. A.7 - Prob. 67E Ch. A.7 - Prob. 68E Ch. A.7 - Average garde. Sean has taken three exams and...Ch. A.7 - Prob. 70E Ch. A.7 - Prob. 71E Ch. A.7 - Prob. 72E

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To solve the given inequality.

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To solve the given inequality.

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Chapter A.7 Solutions