Expert: Ahmed Salami - 4/26/2009

Question
solve: |x+2|>2x

Answer
Hi Anjali,
|x+2| > 2x
First, you have to realise that |x+2| is always positive i.e it is positive for every value of x. For negative values of x, i.e x < 0, 2x is always negative and so we can conclude that
For all x < 0, |x+2| > 2x
Now, for x > 0, both x+2 and 2x are positive and the inequality would only be satisfied when
x+2 > 2x
x < 2
i.e
0 < x < 2
At x = 0, the inequality is also satisfied because
|0+2| > 2(0)
2 > 0
Combining all the resulting intervals, the complete solution is
x < 2

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Regards