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–5 –4 –3 –2 –1 0 1 2 3 (number line shaded portion and X can take any value from -5 until 3) 130. 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

Re: OG 12.problem 130 [#permalink]
05 Dec 2009, 14:34

ISBtarget wrote:

–5 –4 –3 –2 –1 0 1 2 3 (number line shaded portion and X can take any value from -5 until 3) 130. 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

The answer is E, why not B?

b is saying -5≤x≤5 e is saying -5≤x≤3 x+1≤4 = x≤3 -x -1 ≤ 4 -x ≤ 5 x>=-5

Re: OG 12.problem 130 [#permalink]
22 Feb 2010, 00:16

ISB target ....try and put x=4 in eqn 2. It still holds good but doesnt satisfies your number options for the line. Eqn 5 does that for x=4 and is justified only for the numbers given in the quesn.

Re: OG 12.problem 130 [#permalink]
22 Feb 2010, 06:49

ISBtarget wrote:

–5 –4 –3 –2 –1 0 1 2 3 (number line shaded portion and X can take any value from -5 until 3) 130. 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

The answer is E, why not B?

Length = 3-(-5) = 8 center = (-5)+8/2 = -1 Now only D & E has 8/2 = 4 on right side. Also at x=-5 only E is satisfied and not D so answer is E.

Re: OG 12.problem 130 [#permalink]
22 Feb 2010, 07:39

|x+a| <= b

you can take the above case and simplify as below if the origin is at (-a,0) then x will have as many values to the right of -a as to the left of -a. Bacially the values of x are symetric at the value (-a,0)

for the expression given in the question, the values of x are -5<=x<=3 .. the values are symetric at x=-1

so the expression would be a = 1 and b =4 ... |x+1|<=4

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