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Does absolute value n+m= absolute value n + absolute value m for all integers n and m? If so give examples if not give a counterexample.

  • math -

    Only true for m ≥ 0, so in general the statement is false.

    A counterexample for it being true ...
    let n = 10, m = -5

    Left side
    = | 10 - 5| = 5
    right side
    = |10 + |-5| |
    = |10+5|
    = 15

    LS ≠ Rs

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