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Bunuel
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Which inequality below most accurately represents the range of possibl 24 Aug 2015, 23:37
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D
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86% (01:25) correct 14% (01:28) wrong based on 91 sessions

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Which inequality below most accurately represents the range of possible values for x?

A. The absolute value of x is less than or equal to 4.
B. The absolute value of x is less than or equal to 5.
C. The absolute value of (x + 2) is less than or equal to 2.
D. The absolute value of (x – 1) is less than or equal to 3.
E. The absolute value of (x + 1) is less than or equal to 3.


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D
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Which inequality below most accurately represents the range of possibl 25 Aug 2015, 01:22
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Bunuel

Which inequality below most accurately represents the range of possible values for x?

A. The absolute value of x is less than or equal to 4.
B. The absolute value of x is less than or equal to 5.
C. The absolute value of (x + 2) is less than or equal to 2.
D. The absolute value of (x – 1) is less than or equal to 3.
E. The absolute value of (x + 1) is less than or equal to 3.
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Ans: D

Solution: for statements 1) possible range will cover -4 to 4 (2) possible range will cover -5 to 5 (C) Range will cover -4 to 0
(D) range will cover -2 to 4 (E) range will cover -4 to 2
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Which inequality below most accurately represents the range of possibl 26 Aug 2015, 08:28
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Bunuel

Which inequality below most accurately represents the range of possible values for x?

A. The absolute value of x is less than or equal to 4.
B. The absolute value of x is less than or equal to 5.
C. The absolute value of (x + 2) is less than or equal to 2.
D. The absolute value of (x – 1) is less than or equal to 3.
E. The absolute value of (x + 1) is less than or equal to 3.


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IMO : D

Another way is trying to substitute the extreme values in the equation given in the options i.e. (-2) and (4)

Only Option D satisfies the condition.
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Which inequality below most accurately represents the range of possibl 26 Aug 2015, 19:22
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It looks like the circle is not darkened so it seems a bit off.

| x - 1 | <= 3
as x<=4 and x>= -2

But the answer should be

D. The absolute value of (x – 1) is less than or equal to 3.
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Which inequality below most accurately represents the range of possibl 27 Aug 2015, 20:33
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Total distance between value of x is 4-(-2)= 6; hence point 1 will be equidistant with x; and 1 on the number line is 3 point equidistant with -2 and 4.
hence we can write equation as l(x-1)l=<3
Hence answer is D
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Which inequality below most accurately represents the range of possibl 28 Aug 2015, 07:24
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the value of x = (-2 =< x <= 4)

option A-- only upper limit is given . Lower limit not given ----hence wrong .
as x less than or equal to 4

Option B.The absolute value of x is less than or equal to 5. ----crossing the upper limit .

option C . The absolute value of (x + 2) is less than or equal to 2.
take any value of x from the number line and put in the equation ( x+2) it not satisfy ---this condition (-2 =< x <= 4)

option D . The absolute value of (x – 1) is less than or equal to 3. --- same reason C

option E The absolute value of (x + 1) is less than or equal to 3.-----take any value of x from the number line and put in the equation ( x+1 )
it will satisfy the condition ---the value of x = (-2 =< x <= 4)
Hence E ans
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Which inequality below most accurately represents the range of possibl 30 Aug 2015, 09:45
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Bunuel

Which inequality below most accurately represents the range of possible values for x?

A. The absolute value of x is less than or equal to 4.
B. The absolute value of x is less than or equal to 5.
C. The absolute value of (x + 2) is less than or equal to 2.
D. The absolute value of (x – 1) is less than or equal to 3.
E. The absolute value of (x + 1) is less than or equal to 3.


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GROCKIT OFFICIAL SOLUTION:

The first thing we want to do is determine the midpoint between the endpoints. What this does is create an equal distance in the negative and positive directions from that center location. For this question, the center point between -2 and +4 is +1.

From +1, our range of possible values for x extends at most 3 in either direction, but can also be 1, 1.5, 2.8 etc in either direction. This means that the distance from +1 is LESS THAN 3.

Looking at our answer choices, we now have to decide between D and E. With absolute values, as with some advanced pre-calculus equations, the shift within the equation is opposite of the shift on the graph. A good way to quickly test this is to plug in numbers toward the extremes and see which fit.

For (E), if we plug in x = 3.5 (which we know is within the given range) into | x + 1 | ≤ 3, we get 4.5 ≤ 3, which is false.

Any x within the given range meets the inequality | x – 1 | ≤ 3 in Choice D. Be sure to think of ranges in terms of both inequalities and absolute values, as these come up in about 1-2 questions per test.
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Which inequality below most accurately represents the range of possibl 15 Sep 2015, 04:20
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It was my understanding that a white circle on a number line indicates less than or greater than, whereas a black circle indicates less than or equal to or greater than or equal to.
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