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What is the solution set for the inequality -2|3-2x| < 14?

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NYC5648
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What is the solution set for the inequality -2|3-2x| < 14? [#permalink] New post   14 Mar 2012, 12:42
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What is the solution set for the inequality -2|3-2x| < 14?

A. -11/2 < x < 17/2

B. -5 < x < 2

C. -2 < x < 5

D. All values of x satisfy the inequality

E. No values of x satisfy the inequality
 
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D
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What is the solution set for the inequality -2|3-2x| < 14? [#permalink] New post   14 Mar 2012, 13:03
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What is the solution set for the inequality \(-2|3-2x| < 14?\)

A. -11/2 < x < 17/2

B. -5 < x < 2

C. -2 < x < 5

D. All values of x satisfy the inequality

E. No values of x satisfy the inequality

\(-2*|3-2x|=negative*nonnegative=nonpositive\), which is ALWAYS less than positive number 14. So, this inequality holds true for any \(x\).­

Answer: D.
­
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Re: What is the solution set for the inequality -2|3-2x| < 14? [#permalink] New post   16 Mar 2012, 04:27
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shankar245 wrote:
Hi Buneul,
Why cant we do as we do normally as in
take a positive solution , then a negative solution?

x<5
x>-2

What am i doing wrong here?


If you do it properly you'll get the same answer. But you don't need that.

Consider this: \(-2*|3-2x|<14\) --> reduce by negative -2 and flip the sign: \(|3-2x|>-7\) --> LHS is an absolute value, which is always nonnegative, so \(|3-2x|\) will always be more than negative -7, so it'll be more for all values of \(x\).

Hope it's clear.
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optimisttageja
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Re: What is the solution set for the inequality -2|3-2x| < 14? [#permalink] New post   15 Mar 2012, 01:41
|3-2x| can have two possible solns, either it is (3-2x) or -(3-2x) so wr can solve this ques as

-2*(3-2x)<14 => x<5
or
-2*-(3-2x)<14 => x>-4

combining above two

-4is the solution.

Posted from my mobile device
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Re: What is the solution set for the inequality -2|3-2x| < 14? [#permalink] New post   15 Mar 2012, 01:48
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optimisttageja wrote:
|3-2x| can have two possible solns, either it is (3-2x) or -(3-2x) so wr can solve this ques as

-2*(3-2x)<14 => x<5
or
-2*-(3-2x)<14 => x>-4

combining above two

-4
is the solution.

Posted from my mobile device


Sometimes it's a good idea to check whether your solution is correct by plug-in method. So, plug x=10 or x=-10 and see whether the inequality holds true.

Refer for the correct solution above.

Hope it helps.
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Re: What is the solution set for the inequality -2|3-2x| < 14? [#permalink] New post   15 Mar 2012, 02:16
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Yes i guess my soln was wrong.. x could take values -infinity to infinity..

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Re: What is the solution set for the inequality -2|3-2x| < 14? [#permalink] New post   15 Mar 2012, 12:33
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Hi Buneul,
Why cant we do as we do normally as in
take a positive solution , then a negative solution?

x<5
x>-2

What am i doing wrong here?
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Re: What is the solution set for the inequality -2|3-2x| < 14? [#permalink] New post   05 Dec 2012, 03:08
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-2|3-2x| < 14
|3-2x| > -7

What value of x will satisfy the equation? Any value since |3 - 2x| is always positive no matter what value of x.
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Re: What is the solution set for the inequality -2|3-2x| < 14? [#permalink] New post   23 Jan 2016, 05:29
umm, i get -2<x<5

-2|3-2x|<14

solution 1
-2*(3-2x)< 14
-6+4x<14
4x<14+6
4x<20
x<5

solution 2
-2*-1(3-2x)<14
6-4x<14
6-14<4x
-8<4x
-2<x

-2<x<5
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Re: What is the solution set for the inequality -2|3-2x| < 14? [#permalink] New post   10 Jun 2023, 09:32
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Re: What is the solution set for the inequality -2|3-2x| < 14? [#permalink]
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