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Solve each inequality algebraically.

|2x-1|-2<3 I don't understand how the answer is -2<x<3

  • Math -

    There are two important points involved:
    1. When an inequality is multiplied or divided by a negative number on each side, the inequality changes direction.
    For example:
    4<5
    -4>-5

    2. When the absolute function comes into play, we have two conditions which have to be considered separately:
    a. the contents of the absolute function is positive, and
    b. the content of the absolute function is negative.
    This means we double the number of conditions.
    For example, to solve
    |x-1|>4
    we have
    a. x-1>4, => x>5, and
    b. -(x-1) > 4, therefore
    (x-1) <-4
    x<-3

    Apply the same way to the given inequation and you should arrive at
    -2<x<3 as the answer.

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