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# Which of the following inequalities is equivalent to

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Which of the following inequalities is equivalent to [#permalink]

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25 Aug 2003, 20:20
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Which of the following inequalities is equivalent to тАУ2 < x < 4 ?
(A) | x тАУ 2 | < 4
(B) | x тАУ 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above
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01 Sep 2003, 04:34
Which of the following inequalities is equivalent to тАУ2 < x < 4 ?
(A) | x тАУ 2 | < 4
(B) | x тАУ 1 | < 3
(C) | x + 1 | < 3
(D) | x + 2 | < 4
(E) None of the above.

Hi,
Its good to keep the following in mind when solving such problems
|x|-z<0 implies
-z<x<z

Likewise,
|x|-z>0 implies x<-z or x>z

Now, we are given that -2<x<4
(A) => -4<x тАУ 2 < 4
=> -2<x< 6 Not the answer
(B) => -3 < x тАУ 1 < 3
=> -2<X<4 Bingo!!!!

Hope you're convinced.

Andy
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19 Jan 2004, 18:57
I just squared both the sides of the inequalities of given choices and only B gives the roots of X such that -2<x<4
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19 Jan 2004, 19:13
Yes, I approached the problem like Anand Kannan did.

B) | x тАУ 1 | < 3 which translates into

-3 < x - 1 < 3 ---> -2 < x < 4 which is the answer.
Hi   [#permalink] 19 Jan 2004, 19:13
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