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# Find the solution set for the following inequality -2|3-2x|

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Find the solution set for the following inequality -2|3-2x| [#permalink]

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14 Mar 2012, 12:42
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Hi everybody,

can please s.o. help me with this question?

Many thanks

Find the solution set for the following inequality -2|3-2x| < 14?
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Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

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14 Mar 2012, 13:03
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NYC5648 wrote:
Hi everybody,

can please s.o. help me with this question?

Many thanks

Find the solution set for the following inequality -2|3-2x| < 14?

Is it: $$-2*|3-2x|<14$$? If yes, then $$-2*|3-2x|=negative*nonnegative=nonpositive$$, which is ALWAYS less than positive number 14. So this inequality holds true for any $$x$$.
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Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

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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

-4<x<5
is the solution.

Posted from my mobile device
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Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

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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<x<5
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: Find the solution set for the following inequality -2|3-2x| [#permalink]

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15 Mar 2012, 02:16
Yes i guess my soln was wrong.. x could take values -infinity to infinity..

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Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

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15 Mar 2012, 12:33
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: Find the solution set for the following inequality -2|3-2x| [#permalink]

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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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Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

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17 Mar 2012, 06:45
I have a general question.

If I have an inequality with an absolute value expression, why can't I simplify the absolute value expression.

First I can devide by -2, which gives me |3-2x|>-7

Now why can't I check the two cases for the absolute value expression that I have to check when absolute value expression are in equalities?
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Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

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17 Mar 2012, 07:53
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BN1989 wrote:
I have a general question.

If I have an inequality with an absolute value expression, why can't I simplify the absolute value expression.

First I can devide by -2, which gives me |3-2x|>-7

Now why can't I check the two cases for the absolute value expression that I have to check when absolute value expression are in equalities?

Please read my responses above: YOU DO NOT NEED TO DO THAT, since LHS is an absolute value then it's ALWAYS more than negative number -7, so it'll be more for ALL values of x.
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Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

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05 Dec 2012, 03:08
-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: Find the solution set for the following inequality -2|3-2x| [#permalink]

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05 Nov 2014, 08:10
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Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

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26 Nov 2015, 00:13
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Re: Find the solution set for the following inequality -2|3-2x| [#permalink]

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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
Re: Find the solution set for the following inequality -2|3-2x|   [#permalink] 23 Jan 2016, 05:29
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