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Exercise 1. For 2 < x, it is true that 1 1 1 + x4 (1.1) Let's work through the proof to see why (1.1) is true. WVe will start with the assumption that 2 < x. We then use a more simple, true inequality, along with a step-by-step process, to build up to (1.1). (1) To start, we know that when 2

Exercise 1. For 2 < x, it is true that 1 1 1 + x4 (1.1) Let's work through the proof to see why (1.1) is true. WVe will start with the assumption that 2 < x. We then use a more simple, true inequality, along with a step-by-step process, to build up to (1.1). (1) To start, we know that when 2

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.7: Graphing Linear Inequalities
Problem 11OE
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Exercise 1. For 2 < x, it is true that 1 1+ x4° 1 1 (1.1) Let's work through the proof to see why (1.1) is true. WVe will start with the assumption that 2 < x. We then use a more simple, true inequality, along with a step-by-step process, to build up to (1.1). (1) To start, we know that when 2 <x we must have 0 < . (Why? Convince yourself!) (2) adding 1 to both sides of 0 < 4 we obtain (3) after taking the square root of both sides of your answer in (2.) (since they're positive (why?)), we have (4) Now multiply both sides of your answer in (3.) by , which is positive (why?) to obtain the desired result We have successfully shown that (1.1) is true using familiar mathematical operations.
Transcribed Image Text:Exercise 1. For 2 < x, it is true that 1 1+ x4° 1 1 (1.1) Let's work through the proof to see why (1.1) is true. WVe will start with the assumption that 2 < x. We then use a more simple, true inequality, along with a step-by-step process, to build up to (1.1). (1) To start, we know that when 2 <x we must have 0 < . (Why? Convince yourself!) (2) adding 1 to both sides of 0 < 4 we obtain (3) after taking the square root of both sides of your answer in (2.) (since they're positive (why?)), we have (4) Now multiply both sides of your answer in (3.) by , which is positive (why?) to obtain the desired result We have successfully shown that (1.1) is true using familiar mathematical operations.
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