Answer Solution set of given inequality is 1 ≤ x ≤ 2 . Explanation Given information: n 2 + 2 ≤ 3 n n 2 + 2 ≤ 3 n n 2 + 2 ≤ 3 n ⇒ n 2 + 2 − 3 n ≤ 3 n − 3 n ⇒ n 2 − 3 n + 2 ≤ 0 ⇒ n 2 − n − 2 n + 2 ≤ 0 ⇒ n ( n − 1 ) − 2 ( n − 1 ) ≤ 0 ⇒ ( n − 1 ) ( n − 2 ) ≤ 0 If ( x − a ) ( x − b ) ≤ 0 and a < b then a ≤ x ≤ b . Therefore, Solution set of given inequality is 1 ≤ x ≤ 2 .

Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.1, Problem 11MRE

To determine

To find: Solution set of each inequality.

Expert Solution & Answer

Answer to Problem 11MRE

Solution set of given inequality is 1≤x≤2 .

Explanation of Solution

Given information:

n2+2≤3n

n2+2≤3n⇒n2+2−3n≤3n−3n⇒n2−3n+2≤0⇒n2−n−2n+2≤0⇒n(n−1)−2(n−1)≤0⇒(n−1)(n−2)≤0

If (x−a)(x−b)≤0 and a<b then

a≤x≤b .

Therefore,

Solution set of given inequality is 1≤x≤2 .

Chapter 5.1, Problem 10MRE

Chapter 5.1, Problem 12MRE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OE Ch. 5.1 - Prob. 2OE Ch. 5.1 - Prob. 3OE Ch. 5.1 - Prob. 4OE Ch. 5.1 - Prob. 5OE Ch. 5.1 - Prob. 6OE Ch. 5.1 - Prob. 7OE Ch. 5.1 - Prob. 8OE Ch. 5.1 - Prob. 9OE Ch. 5.1 - Prob. 10OE

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