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Which of the following inequalities is equivalent to -2 <

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Intern
Joined: 26 Mar 2003
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Which of the following inequalities is equivalent to -2 < [#permalink]

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09 May 2003, 16:41
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Which of the following inequalities is equivalent to -2 < x < 4?

(a) |x-2|<4
(b) |x-1|<3
(c) |x+1|<3
(d) |x+2|<4
(e) None of the above

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CTO
Joined: 19 Dec 2002
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Location: Ukraine

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10 May 2003, 00:26
-2 + a = -(4 + a)
-2 + a = -4 - a
2a = -2
a = -1

-2 - 1 = -(4 - 1)

-2 < x - 1 < 4
<=>
-2 - 1 < x - 1 < 4 - 1
<=>
-3 < (x-1) < 3
<=>
|x-1| < 3

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Intern
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10 May 2003, 22:13
gravedigger wrote:
-2 + a = -(4 + a)
-2 + a = -4 - a
2a = -2
a = -1

-2 - 1 = -(4 - 1)

-2 < x - 1 < 4
<=>
-2 - 1 < x - 1 < 4 - 1
<=>
-3 < (x-1) < 3
<=>
|x-1| < 3

What does the first statement mean? I am somewhat confused....

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CTO
Joined: 19 Dec 2002
Posts: 250

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11 May 2003, 02:20
my idea was to normalize the inequality to a form of
-N < (x - K) < N

this could be achieved by adding some number, but the number itself is yet unknown. Let it be "a":

2 < x - 1 < 4
<=>
-2 + a < x - 1 + a < 4 + a

that's how i got
-2 + a = 4 + a

I do it simply to find what number to add to the ineq. In this case it's faster just to pick it, but i just wanted to show that it can be derived.

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Senior Manager
Joined: 17 Apr 2005
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04 Jul 2005, 07:06
kdog3490 wrote:
Which of the following inequalities is equivalent to -2 < x < 4?

(a) |x-2|<4
(b) |x-1|<3
(c) |x+1|<3
(d) |x+2|<4
(e) None of the above

B.

for x > 1. (b) reduces to x - 1 < 3 or x < 4
for x < 1. (b) reduces to 1- x < 3 or x > -2
also (b) holds when x = 1 hence , reduces to -2 < x < 4.

HMTG.

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Re: PS: Inequality   [#permalink] 04 Jul 2005, 07:06
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