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# How to solve an inequality with abs. value?

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

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- sahsjingLv 78 years agoFavorite 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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- Anonymous8 years ago
x < -1 or x > 1/3

Source(s): I took Algebra 2 last year.- Login to reply the answers

- ?Lv 48 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.- Login to reply the answers

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