Explanation Given inequality is | a − b | < | a | + | b | . Case 1: Consider 0 < a ≤ b . Substitute any positive values for a and b in given inequality as follows. | a − b | < | a | + | b | | 2 − 4 | < | 2 | + | 4 | [ Let a = 2 , b = 4 ] | − 2 | < 2 + 4 1 < 6 The condition of 0 < a ≤ b satisfies the inequality | a − b | < | a | + | b | . Case 2: Consider 0 < b ≤ a . Substitute positive values for a and b in given inequality as follows. | a − b | < | a | + | b | | 4 − 2 | < | 4 | + | 2 | [ Let a = 4 , b = 2 ] | 2 | < 4 + 2 2 < 6 The condition of 0 < b ≤ a satisfies the inequality | a − b | < | a | + | b | . Case 3: Consider a ≤ b < 0 . Substitute negative values for a and b in given inequality as follows. | a − b | < | a | + | b | | ( − 2 ) − ( − 1 ) | < | − 2 | + | − 1 | [ Let a = − 2 , b = − 1 ] | − 2 + 1 | < 2 + 1 | − 1 | < 3 1 < 3 The condition of a ≤ b < 0 satisfies the inequality | a − b | < | a | + | b | . Case 4: Consider b ≤ a < 0 . Substitute negative values for a and b in given inequality as follows

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 17, Problem 64RE

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The condition under which the inequality |a−b|<|a|+|b| is satisfied.

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Chapter 17, Problem 63RE

Chapter 17, Problem 65RE

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Chapter 17 Solutions

Basic Technical Mathematics

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The condition under which the inequality | a − b | &lt; | a | + | b | is satisfied.

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The condition under which the inequality |a−b|<|a|+|b| is satisfied.

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Chapter 17 Solutions

The condition under which the inequality | a − b | < | a | + | b | is satisfied.