Which of the following inequalities is an algebraic expression for the

Question

https://gmatclub.com/forum/download/file.php?id=40653 Which of the following inequalities is an algebraic expression for the graph shown? (-3 and 4 are not included in the range) A. |x - \frac{1}{2}| < \frac{7}{2} B. |x - \frac{1}{2}| > \frac{7}{2} C. |x - \frac{1}{2}| \leq \frac{7}{2} D. |x - \frac{1}{2}| \geq \frac{7}{2} E. |2x - \frac{1}{2}| < \frac{7}{2} 2018-04-01_2151.png

DavidTutorexamPAL · Accepted Answer

We'll use the underlying symmetry of an inequality with absolute value.
This is a Logical approach.

All our answers are of the form |x + a| <b.
This can be written as -b < x+a < b.
So, we'd like to rewrite our original expression, -3 < x < 4, so that the number on the left and that on the right are the same.
We can SEE that if we subtract 1/2 from all sides we get -3.5 < x - 1/2 < 3.5 which is what we want.
Then |x - 1/2| <3.5 is our answer.
(A) is our answer.

GMATBusters · Answer

Steps to convert inequality graph to algebraic expression:

1) Plot the midpoint (a) of the solution set on the number line:
here the midpoint, a = (-3+4)/2 = 1/2

2) Find the distance (b unit) of either end points from the mid point :
here the distance, b = 4-1/2 = 7/2

3) Insert the appropriate sign of inequality between |x-a| and b:

appropriate sign can be taken from this:

Here , putting a and b, we get |x-1/2|<7/2

hence, the Required inequality is |x-1/2|<7/2

Answer = A

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kunalcvrce · Answer

from graph we can get -3<x<4

with option 1 --> -7/2<x-1/2<7/2 solving -3<x<4

hence option A

MT1988 · Answer

Easiest way i think is by inputting values
input 0

A.  |x - \frac{1}{2}| < \frac{7}{2} 
 Pass 
B.  |x - \frac{1}{2}| > \frac{7}{2} 
 Fails 
C.  |x - \frac{1}{2}| \leq \frac{7}{2} 
 Pass 
D.  |x - \frac{1}{2}| \geq \frac{7}{2} 
 Fails 
Fails as -3 is not in the range and this option gives RHS = LHS at -3.
E.  |2x - \frac{1}{2}| < \frac{7}{2} 
 Pass

Input -3 in A, C and E

A.  |x - \frac{1}{2}| < \frac{7}{2} 
 Pass

C.  |x - \frac{1}{2}| \leq \frac{7}{2} 
 Fails

E.  |2x - \frac{1}{2}| < \frac{7}{2} 
 Fails 
  |2*-3 - \frac{1}{2}| = |-6 - \frac{1}{2} | = |\frac{-13}{2}| = \frac{13}{2}which is greater than \frac{7}{2}  proving the option wrong.

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Kinshook · Answer

Mid point =  \frac{1}{2} 
Distance from either side =  \frac{7}{2} 
End points exclusive

|x-\frac{1}{2}| < \frac{7}{2}

IMO A

TBT · Answer

Can the above method to convert graph to algebric equation always be used?

bumpbot · Answer

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Which of the following inequalities is an algebraic expression for the

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Which of the following inequalities is an algebraic expression for the

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