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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  [#permalink]

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New post 01 Apr 2018, 10:55
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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. \(|2x - \frac{1}{2}| < \frac{7}{2}\)


Attachment:
2018-04-01_2151.png
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Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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New post 01 Apr 2018, 11:09
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Bunuel wrote:
Image

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. \(|2x - \frac{1}{2}| < \frac{7}{2}\)

Attachment:
2018-04-01_2151.png


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.
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Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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New post 01 Apr 2018, 11:06
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Bunuel wrote:
Image

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. \(|2x - \frac{1}{2}| < \frac{7}{2}\)




Attachment:
2018-04-01_2151.png


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
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Which of the following inequalities is an algebraic expression for the  [#permalink]

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New post 01 Apr 2018, 11:27
Bunuel wrote:
Image

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. \(|2x - \frac{1}{2}| < \frac{7}{2}\)


Attachment:
2018-04-01_2151.png


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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Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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New post 27 Sep 2018, 10:12
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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:
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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Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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New post 19 Aug 2019, 05:09
Bunuel wrote:
Image

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. \(|2x - \frac{1}{2}| < \frac{7}{2}\)



Attachment:
2018-04-01_2151.png


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

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

IMO A
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Re: Which of the following inequalities is an algebraic expression for the   [#permalink] 19 Aug 2019, 05:09
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