Which of the following is the solution set for the inequality 0

Question

Which of the following is the solution set for the inequality  0<|x|-2x<3 ?

A.  -1<x<0

B.  0<x<1

C.  1<x<2

D.  2<x<3

E.  3<x<4

lucajava · Accepted Answer

0 < |x| -2x < 3

Case A :  x ≥ 0

0 < -x < 3 
 -3 < x< 0

There are no solutions here since  x ≥ 0 .

Case B :  x < 0

0 < -3x < 3 
 0 < -x < 1 
 -1 < x < 0

That's what we were looking for. Hence,  A .

GMATGuruNY · Answer

We can PLUG IN THE ANSWERS, which represent the range of x.

A: -1 < x < 0
Plugging x=-0.5 into the given inequality, we get:
0 < |-0.5| - 2(-0.5) < 3
0 < 0.5 + 1 < 3
0 < 1.5 > 3
Since x=-0.5 is a valid solution, the correct answer must include x=-0.5 within its range.
Eliminate B, C, D and E.

A .

Rogerkille · Answer

When solving the absolute value inequality after x I got:

0>x>-3
0>x>-1

MathRevolution · Answer

=>

By definition, if  x ≥ 0 , then  |x| = x  and if  x < 0, |x| = -x.

If  x ≥ 0 , then  0<|x|-2x<3  is equivalent to  0 < x – 2x < 3  or  0 < -x < 3. 
So,  -3 < x < 0 , which does not satisfy the assumption  x ≥ 0 .
If  x < 0 , then  0<|x|-2x<3  is equivalent to  0 < -x -2x < 3  or  0 < -3x < 3. 
Then  -1 < x < 0 , which satisfies the assumption  x < 0. 
Thus, the solution set is  -1<x<0.

Therefore, the answer is A.
Answer: A

shanu777 · Answer

Hi, so when x<0, we are taking negative values of x, so would the equation boil down to 0<-x-(2*(-x))<3 which would equal 0<-x-(-2x)<3---->0<-x+2x<3

I am confused in this part, if you could clarify a little.

thanks

Bunuel · Answer

When x < 0, we have |x| = -x. However, this does not mean that x is replaced with -x; it stays as x.

So, for x < 0, the inequality 0 < |x| - 2x < 3 becomes:
 
0 < (-x) - 2x < 3
 
This simplifies to:
 
0 < -3x < 3
 
After multiplying by -1, we get:
 
-3 < 3x < 0
 
which further simplifies to:
 
-1 < x < 0
 
 10. Absolute Value 
     Theory   
 Math: Absolute value (Modulus) 
 Absolute Value: Tips and hints 
 Properties of Absolute Values on the GMAT 
 Absolute modulus : A better understanding 
 GMAT Question Patterns: Abolute Value 
 The Reason Behind Absolute Value Questions on the GMAT 
     Questions   
 Inequality and absolute value questions from my collection 
 The E-GMAT Question Series on ABSOLUTE VALUE 
 DS Questions 
 PS Questions

For more check  Ultimate GMAT Quantitative Megathread

Hope it helps.

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Which of the following is the solution set for the inequality 0<|x|-2x

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