1. Which conjunction or disjunction is equivalent to the open sentence |a - 8| ≤ 3?. A. a - 8 ≤ 3 and a - 8 ≥ - 3. B. a - 8 ≥ 3 and a - 8 ≤ - 3. C. a - 8 ≤ 3 or a - 8 ≥ - 3. D. a - 8 ≥ 3 or a - 8 ≤ - 3. 2. Which conjunction or disjunction is equivalent to the open sentence 4 - 2|n + 6| ≥ 2?. A. n + 6 ≤ - 1 and n + 6 ≥ 1. B. - 5 < n or n - 5 or n < - 7. 3. Solve the equation. |k + 6| = 3. A. {-3, 9}. B. {-3, 3}. C. {-9, - 3}. D. {all real numbers greater than or equal to - 9 and less than or equal to - 3}

Question

Mathematics

George Kirby

10 April, 05:21

1. Which conjunction or disjunction is equivalent to the open sentence |a - 8| ≤ 3?. A. a - 8 ≤ 3 and a - 8 ≥ - 3. B. a - 8 ≥ 3 and a - 8 ≤ - 3. C. a - 8 ≤ 3 or a - 8 ≥ - 3. D. a - 8 ≥ 3 or a - 8 ≤ - 3. 2. Which conjunction or disjunction is equivalent to the open sentence 4 - 2|n + 6| ≥ 2?. A. n + 6 ≤ - 1 and n + 6 ≥ 1. B. - 5 < n or n - 5 or n < - 7. 3. Solve the equation. |k + 6| = 3. A. {-3, 9}. B. {-3, 3}. C. {-9, - 3}. D. {all real numbers greater than or equal to - 9 and less than or equal to - 3}

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Answers (1)

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Christian Kennedy · Answer 1

The given expressions above are examples of an absolute-value inequality. In the expression |a - 8| ≤ 3, this is equal to - 3 ≤ a - 8 ≤ 3. In this case, the answer here in 1 is A. a - 8 ≤ 3 and a - 8 ≥ - 3. in 2, the expression is 4 - 2 (n + 6) ≥ 2 or - 8 - 2n ≥ 2 or 4 + n ≤ - 1 equal to n ≤ - 5. The other equation is 4 - 2 * - (n + 6) ≥ 2. 16 + 2n ≥ 2 or 8 + n ≥ 1. n ≥ - 7. Answer is n ≤ - 5 or n ≥ - 7. The equation |k + 6| = 3 is equal to k + 6 = 3 or k = - 3 and k+6 = - 3 equal to k = - 9. Answer in 3 is C.