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Which of the following inequalities is an algebraic expressi

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Which of the following inequalities is an algebraic expressi [#permalink] New post 17 Dec 2012, 05:54
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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
[Reveal] Spoiler: OA
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Re: Which of the following inequalities is an algebraic expressi [#permalink] New post 17 Dec 2012, 05:57
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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.

Answer: E.
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Re: Which of the following inequalities is an algebraic expressi [#permalink] New post 31 Dec 2013, 01:17
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Re: Which of the following inequalities is an algebraic expressi [#permalink] New post 11 Jan 2014, 02:18
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Walkabout wrote:
Attachment:
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



Lets try to do this conceptually,

The length of the line is 8. Middle point = 8/2 = 4. The point on the number line equidistant at a length of 4 from each extremeties (-5 and 3) is -1. So, the equation turns out to be,

|x - (equidistant point)| <= Middle Point
i.e. |x-(-1)| <= 4
i.e. |x+1| <= 4

Ans - (E) :-D

Last edited by adeelahmad on 11 Jan 2014, 02:26, edited 1 time in total.
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Re: Which of the following inequalities is an algebraic expressi [#permalink] New post 11 Jan 2014, 02:24
Walkabout wrote:
Attachment:
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


Round 1: Eliminate the obvious, let us say x = -5 and eliminate from options

(A) Eliminated
(B) Okay
(C) Eliminated
(D) Eliminated
(E) Okay

Round 2: We are left between B and E. There are two things you can do.

Use Algebra:
|x| <= 5 - Contains numbers from -5 to +5 which does not define the inequality as 4 and 5 are not part of the inequality

Hence answer is E

OR

Plug in x = 4 where Option B satisfies which was not supposed to be.
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Re: Which of the following inequalities is an algebraic expressi [#permalink] New post 21 Apr 2014, 03:29
yeehaaahhh

tried with bunuel's logic. It worked within 30 sec

calculate length - 8
center - from the graph = -1

only two options have r.h.s = 4 (half of length). Further, in E, LHS becomes zero when x = -1.
Hence, E.
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Re: Which of the following inequalities is an algebraic expressi [#permalink] New post 15 Jun 2014, 23:48
My Approach

Looking at the number line, it can be inferred that the line would have been |x|\leq{4} or -4\leq{x}\leq{4} if it was was centered at 0. (since length = 8 units and end points as +-4)

Now since the line |x|\leq{4} is centered at 0 and in this case is shifted to left by 1 unit (now centered at -1), the equation of the line becomes |x-(-1)|\leq{4}
or |x+1|\leq{4}

Hence E
Re: Which of the following inequalities is an algebraic expressi   [#permalink] 15 Jun 2014, 23:48
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