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6. Given integers a, b, and c, suppose that a-b is even and b-c is even. Determine whether 2a-(b + c) is even or odd, and prove your answer.

6. Given integers a, b, and c, suppose that a-b is even and b-c is even. Determine whether 2a-(b + c) is even or odd, and prove your answer.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 54E
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6. Given integers \(a, b,\) and \(c\), suppose that \(a - b\) is even and \(b - c\) is even. Determine whether \(2a - (b + c)\) is even or odd, and prove your answer.
Transcribed Image Text:6. Given integers \(a, b,\) and \(c\), suppose that \(a - b\) is even and \(b - c\) is even. Determine whether \(2a - (b + c)\) is even or odd, and prove your answer.
Expert Solution
Step 1

Given that a-b and b-c both are even integers, then we determine whether 2a-(b+c) is an even integer or an odd integers.

You may think as two cases, any integers are either even or odd

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