Which inequality below most accurately represents the range of possibl

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.

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

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

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.

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.