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# Which of the following inequalities is an algebraic expression for the

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
Which of the following inequalities is an algebraic expression for the  [#permalink]

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01 Apr 2018, 09:55
00:00

Difficulty:

15% (low)

Question Stats:

75% (01:22) correct 25% (01:44) wrong based on 254 sessions

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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 [ 4.15 KiB | Viewed 1803 times ]

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Location: India
Concentration: General Management, Marketing
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Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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01 Apr 2018, 10:06
1
Bunuel wrote:

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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Joined: 07 Dec 2017
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Re: Which of the following inequalities is an algebraic expression for the  [#permalink]

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01 Apr 2018, 10:09
2
Bunuel wrote:

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

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01 Apr 2018, 10:27
Bunuel wrote:

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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27 Sep 2018, 09:12
1

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

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Re: Which of the following inequalities is an algebraic expression for the   [#permalink] 27 Sep 2018, 09:12
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