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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] New post 14 Mar 2012, 11:42
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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] New post 14 Mar 2012, 12:03
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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] New post 15 Mar 2012, 00:41
|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.

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Re: Find the solution set for the following inequality -2|3-2x| [#permalink] New post 15 Mar 2012, 00:48
Expert's post
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.

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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] New post 15 Mar 2012, 01:16
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] New post 15 Mar 2012, 11:33
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] New post 16 Mar 2012, 03:27
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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] New post 17 Mar 2012, 05:45
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] New post 17 Mar 2012, 06:53
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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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Find the solution set for the following inequality -2|3-2x| [#permalink] New post 05 Dec 2012, 02:08
-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] 05 Dec 2012, 02:08
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