Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 years ago

How to solve an inequality with abs. value?

|x-1|<|2x| the absolute value in both sides threw me off, help please!

3 Answers

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  • 8 years ago
    Favorite Answer

    Step 1. Find boundary points.

    x-1 = 2x => x = -1

    or

    x-1 = -2x => x = 1/3

    Step 2. Check intervals (-inf., -1), (-1, 1/3), (1/3, inf.)

    Step 3. Answer: (-inf., -1) U (1/3, inf.)

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  • Anonymous
    8 years ago

    x < -1 or x > 1/3

    Source(s): I took Algebra 2 last year.
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  • ?
    Lv 4
    8 years ago

    You can rearrange it: |x - 1| < |2x| <=> |x - 1| - |2x| < 0 .

    You face two cases.

    1) (x - 1) and 2x are >0 =>(x - 1) - (2x) < 0.

    2) (x - 1) and 2x are <0 => (-x + 1) - (-2x) < 0.

    Then you solve it for each case.

    Source(s): Hope it'll help.
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