Whenever one has an inequality, an interesting problem is to characterize the cases of equality. Consider the triangle inequality, which says that x + y ≤ x + y for all real numbers x and y. True or false: If x and y are real numbers for which x + y = |x|+|y, then either x and y are both positive, or x and y are both negative, or at least one of the numbers x and y is zero. True False

Whenever one has an inequality, an interesting problem is to characterize the cases of equality. Consider the triangle inequality, which says that x + y ≤ x + y for all real numbers x and y. True or false: If x and y are real numbers for which x + y = |x|+|y, then either x and y are both positive, or x and y are both negative, or at least one of the numbers x and y is zero. True False

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.3: Introduction To Geometric Proof

Problem 36E: The Division Property of Inequality requires that we reverse the inequality symbol when dividing by...

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Similar questions

The Division Property of Inequality requires that we reverse the inequality symbol when dividing by a negative number. Given that 124, form the inequality that results when we divide each side by 4.

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Elementary Geometry For College Students, 7e

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ISBN:

9781337614085

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Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:

Cengage,