To determine To write: The relation between the expressions | x + y | and | x | + | y | if x > 0 and y < 0 . Explanation Property used: 1. Multiplication or division of each member of the inequality by same positive number will not change the sense of the inequality. The property is symbolically denoted as, “if a < b then a c < b c and a c < b c where c > 0 .” 2. For a positive integer n, the sense of the inequality remains unchanged when n th power or n th root is taken for both members of the inequality, provided both members are positive numbers. The property is symbolically denoted as, “if a < b then a n < b n and a n < b n where a , b and n are positive .” Calculation: Let x > 0 and y < 0 . Then x y < 0 and | x | | y | > 0 . Combine the inequalities and obtain x y < 0 < | x | | y | . By property 1, the sense of the inequality x y < | x | | y | remains unchanged, when each member of the inequality is multiplied by 2. Multiply the inequality x y < | x | | y | by 2 as shown below. 2 x y < 2 | x | | y | x 2 + 2 x y + y 2 < x 2 + 2 | x | | y | + y 2 ( Add x 2 and y 2 on both sides ) x 2 + 2 x y + y 2 < | x | 2 + 2 | x | | y | + | y | 2 ( Since x 2 = | x | 2 and y 2 = | y | 2 ) x 2 + x y + x y +

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

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Chapter 17.1, Problem 49E

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To write: The relation between the expressions |x+y| and |x|+|y| if x>0 and y<0.

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Chapter 17.1, Problem 48E

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Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

Ch. 17.1 - For −6 < 3, determine the inequality if 1. 8 is...Ch. 17.1 - Prob. 2PE Ch. 17.1 - For the inequality −6 < 3, state the inequality...Ch. 17.1 - Prob. 4PE Ch. 17.1 - Prob. 5PE Ch. 17.1 - In Exercises 1–4, make the given changes in the...Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - In Exercises 5–12, for the inequality 4 < 9, state...

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The relation between the expressions | x + y | and | x | + | y | if x &gt; 0 and y &lt; 0 .

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The relation between the expressions | x + y | and | x | + | y | if x > 0 and y < 0 .