Which of the following inequalities is equivalent to 2

Question

Which of the following inequalities is equivalent to –2 < x < 4 ?

(A) |x – 2| < 4
(B) |x – 1| < 3
(C) |x + 1| < 3
(D) |x + 2| < 4
(E) None of the above

cicerone · Accepted Answer

Instead of verifying each and every option you can figure out this a bit faster in the following manner |x| < a => -a < x < a . Note that lower limit of x i.e -a and the upper limit of x i.e a essentially sum up to 0 Now if -2 < x < 4, let's say by adding y to this inequality we will get into the above format -2+y < x+y < 4+y Now, to move this into the mod format, we need to have (-2+y) + (4+y) = 0 => y = -1 Thus, -3 < x-1 < 3 => |x-1| < 3. Hence, B

GoLeafsGo · Answer

Expand the inequality to remove the absolute value from the expression:

(A) | x – 2 | < 4
Two expressions:
x - 2 < 4 simplifies to x < 6
x - 2 >-4 simplifies to x > -2
Therefore, -2 < x < 6 is not equal to -2 < x < 4 NOT THE ANSWER

(B) | x – 1 | < 3
Two expressions:
x - 1 < 3 simplifies to x < 4
x - 1 > -3 simplifies to x > -2
Therefore, -2 < x < 4 is equal to -2 < x < 4 THIS IS THE ANSWER

(C) | x + 1 | < 3
Two expressions:
x + 1 < 3 simplifies to x < 2
x + 1 > -3 simplifies to x > -4
Therefore, -4 < x < 2 is not equal to -2 < x < 4 NOT THE ANSWER

(D) | x + 2 | < 4
Two expressions:
x + 2 < 4 simplifies to x < 2
x + 2 > -4 simplifies to x > -6
Therefore, -6 < x < 2 is not equal to -2 < x < 4 NOT THE ANSWER

(E) None of the above
Since B is the answer, E cannot be correct

camlan1990 · Answer

(A) | x – 2 | < 4 => -2 –2 < x < 4: yeah (C) | x + 1 | < 3 => -4 -6

stonecold · Answer

The only golden rule needed to solve this excellent question => |x|<n => x lies in the range (-x,x)

LogicGuru1 · Answer

There is a super easy method to solve such question First remove the mod then set the expression to 0 then get a value of X then add and subtract the value from the given number on the RHS Lets try with an example (B) --------------> | x – 1 | < 3 First remove the mod -------------------> x-1 then set the expression to 0--------------> x-1=0 then get a value of x---------------------> x=1 then add and subtract the value from the given number on the RHS 1+3=4 and 1-3= -2 the range become -2 to 4 correct answer Now try its with an incorrect option (C) | ----------> |x + 1 | < 3 First remove the mod --------------------------> x+1 then set the expression to 0----------------------> x+1=0 then get a value of x------------------------------> x=-1 then add and subtract the value from the given number on the RHS -1+3=2 and -1-3= -4 the range become -4 to 2 Incorrect THE CORRECT ANSWER IS B

nishantt7 · Answer

The best way to do this question would be through number line.

Option b says distance of point x from 1 should be less than 3 which means from 1 you can move to the right till 4 and from 1 you can move left till -2 so that the distance from 1 stays less than 3.
-2<x<4.

Ophelia__ · Answer

Note: | x – 3 | < 1 represents the distance from x to 3 is less than 1. On a number line, 3 is the mid-point, x is within the range of one unit to the left of 3 and one unit to the right of 3. Therefore, 2<x<4.

Question ask: Which of the following inequalities is equivalent to –2 < x < 4 ?

We can reverse engineer the equation. From –2 < x < 4, we can find the mid-point is 1, and x is within the range of 3 units to the left and 3 units to the right. Then, it is quite straightforward to see the answer is B. | x – 1 | < 3

samriddhi1234 · Answer

here's how I solved it:

to get the midpoint between the range, you can add -2 and 4 and divide by 2 which gives us 1, which is the origin. 
so now you know the expression has to be |x-1| which is the standard form, and the distance from 1 to 4 and 1 to -2 is just under 3 so B is the answer.

Which of the following inequalities is equivalent to 2 < x < 4 ?

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