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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:

    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
    we have
    a. x-1>4, => x>5, and
    b. -(x-1) > 4, therefore
    (x-1) <-4

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

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