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# Which of the following inequalities is an algebraic

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

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11 May 2009, 01:58
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number line.png [ 3.24 KiB | Viewed 12040 times ]
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-inequalities-is-an-algebraic-expressi-144267.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Jun 2014, 00:57, edited 2 times in total.
Renamed the topic and edited the question.

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

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04 Dec 2012, 03:50
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tejal777 wrote:
Attachment:
number line.png
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

From the number line it follows that $$-5\leq{x}\leq{3}$$

(A) |x| <= 3 --> $$-3\leq{x}\leq{3}$$. Discard.

(B) |x| <= 5 --> $$-5\leq{x}\leq{5}$$. Discard.

(C) |x - 2| <= 3 --> $$-3\leq{x-2}\leq{3}$$ --> add 2 to all parts: $$-1\leq{x}\leq{5}$$. Discard.. Discard.

(D) |x - 1| <= 4 --> $$-4\leq{x-1}\leq{4}$$ --> add 1 to all parts: $$-3\leq{x}\leq{5}$$. Discard.. Discard.

(E) |x +1| <= 4 --> $$-4\leq{x+1}\leq{4}$$ --> subtract 1 from all parts: $$-5\leq{x}\leq{3}$$. OK.

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

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11 May 2009, 04:05
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For mods, you always have to take 2 values

(1)x+1 <=4
>> x <=3

(2) -(x+1) <=4
>> -x-1<=4
>> -x<=5
(multiple by - on both the sides, signs flips)
>> x>=-5

E

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

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11 May 2009, 02:16
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x = 4, which is outside of the shaded area, also satisfies b. Therefore you can eliminate b since it applies to the shaded area and then some.

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04 Dec 2012, 01:35
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There is a pattern to figuring out absolute value inequalities.

(See image)

The expression in the absolute value sign helps you figure out the center.
For example: |x-3| < 5
This means 3 is at the center of the range.
Mark x = 3+5 = 8
Mark x = 3-5 = -2
The < sign tells us that x is within x={-2,8} range but not inclusive.

Another example: |x+3|>5
This means -3 is at the center of the range.
Mark x = -3+5 = 2
Mark x = -3-5 = -8
The > sign tells us that x is not within but outside range x={2,-8}
Attachments

absvalue.jpg [ 9.6 KiB | Viewed 11979 times ]

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

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28 Aug 2010, 08:54
Trial & error i.e., back solving is the best way to solve the problem.
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Re: Which of the following inequalities is an algebraic [#permalink]

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21 Nov 2011, 10:04
We need to find the center point in the shaded part of the number line.

Here it is easy to identify that -1 is the center point and the region is 4 units from it on either side.

So x is less than 4 units on either side of -1
this gives $$|x+1|<=4$$.

Ans: e

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

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04 Dec 2012, 01:45
There is a pattern to solving this question.

1) Get the center of the range
c = (-5 + 3)/2 = -2/2 = -1
2) Flip the sign and append variable x
|x + 1|
3) Get the distance of the center to one end
d = 3-(-1) = 4
4) To decide the sign, we know that the value of x is within range inclusive of both ends. We use "<="

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

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07 Dec 2013, 18:49
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Re: Which of the following inequalities is an algebraic [#permalink]

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25 Mar 2014, 13:25
tejal777 wrote:
Attachment:
number line.png
Which of the following inequalities is an algebraic expression for the shaded part of the number line above?

(A) |x| <= 3
(B) |x| <= 5
(C) |x - 2| <= 3
(D) |x - 1| <= 4
(E) |x +1| <= 4

Sol: lets try finding the origin for this graph
(3-(-5)) = 8 units
so total number of points are 9 so the origin must be the 5th point which +1.
only E fits

OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-inequalities-is-an-algebraic-expressi-144267.html

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Re: Which of the following inequalities is an algebraic   [#permalink] 25 Mar 2014, 13:25
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