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10 June, 08:10

How to simplify |x + 120| when x < - 120

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Answers (2)
  1. 10 June, 08:34
    0
    Start with definition of absolute value, |x|.

    It says,

    |x| = x, for any x > = 0 and

    |x| = - x, for any x < 0

    Now, instead of x, we have the expression x+120 inside the absolute value brackets:

    |x+120|

    Play the same game as above - what is the absolute value here?

    |x+120| = x+120 for (x+120) >=0 and

    |x+120| = - (x+120) for (x+120) <0

    Now, recognize that the last condition (x+120) <0 is the same as writing x<-120. That is the condition in the question. Therefore the absolute value |x+120| will equal the second expression (for that condition), namely - (x+120), or - x-120.
  2. 10 June, 08:40
    0
    Step-by-step explanation:

    When x < - 120, the quantity x + 120 is less than zero (is negative).

    To gain the same result as |x + 120|, rewrite |x + 120| as - (x + 120). As we know, the negative of a negative quantity is positive.
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