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Confusing modulus question

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    Hi everyone,

    I have been given the following problem:

    | x + 2 | < 3 => |x| <1

    According to the worksheet there's a counterexample to this statement, but I can't find one - can anyone else find one, or is it me being silly?
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    Have you tried drawing a number line and thinking about lengths? Try not to think about |x| < 1 => |x+2| < 3 because that is a different statement.
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    (Original post by Electrogeek)
    Hi everyone,

    I have been given the following problem:

    | x + 2 | < 3 => |x| <1

    According to the worksheet there's a counterexample to this statement, but I can't find one - can anyone else find one, or is it me being silly?
    Minus 2 does not work
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    | x + 2 | < 3 --> -3 < x + 2 < 3 --> -5 < x < 1
    x in (-5, -1] would be a counter example to the statement, if the problem stated that | x + 2 | < 3 is only true for |x| < 1.
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    AH... So the counter example is to show that the rule exceeds the |x| <1 (because the domain where the equation is true is -5< x < 1)
 
 
 
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