If -|x| = b, where b is a non-zero integer, which of the following sta

3 conditions

1. b obviously can take any value
2. b=-1, x=-1 results in -|x|=b, -1=-1 and satisfies x<-b
3. b=-1, x=1 results in -|x|=b, -1=-1 and satisfies x>b

I)
-|x| = b

Since b or x are non-zero integer, |x|>0.

hence, -|x| <0
b<0 (always true)
Must be true

II)

If x is negative, x< -b . (-b is always positive)

Can be true

III)

If x is positive, x>b (b is always negative)

Can be true

Q comes down to Analyzing the Modulus and the Output/Outcome

(1st) we are told that B = a NON-Zero Integer

Given:

(-)[X] = B

X must also be = a NON-Zero Integer


(2nd)

(-)[X] = B

The OUTPUT of the Modulus [X] must be (+)Pos. since X can NOT be 0

(-)[X] = (-) * (+Pos. Integer Output) = (-)Negative Integer = B

thus, we know for Sure that B must be a (-)Negative Integer

I not only can be true: I must be True



II. X < (-)B

Since we know that B must = (-)Negative Integer:

The Expression (-)B ------> (-) * (-Neg. Integer) = (+)Positive Integer

If the INPUT X into the Modulus is (-)Negative, then we can have a case where ----> X < (-)B

Case: X = (-)5

(-) * [-5] = B
(-) * +5 = B

B = (-)5

and therefore ------> (-)B = (-) * (-5) = +5

X = (-)5 -------- and ------- (-)B = +5

it can be true that: X < (-)B

II can be True




III. X > B

Again, since we know that B must be = (-)Neg. Integer

If the Input X = (+)Pos. Integer, then we can easily Find a Case where X > B

Case:
Given ----> (-) * [X] = B

If X = +2

(-) * [+2] = B

(-) * +2 = B

B = (-)2

X (+2) > B (-2)

III. Can be True



-E-

I, II, and III all can be True

a) |x|=-b, so b is surely negative, as b is non-zero. However x can be both positive and negative.
Clearly I is MUST be true.

b) If x is negative, then x=b, and x=b<-b
II can be true, when x<0

c)If x is positive, then x=-b, and x=-b>b
III can be true, when x>0

All three CAN be true.

E

Hi chetan2u ,

Could you please take any example , such as any internet value for x and b and explain the same ..

I don’t know why I am getting confused everytime while seeing this question

At times , I am thinking that
-|x| = b means b is negative so -|x| = -b which Means |x| = b is what we have in the given part .

Now , option [1] is alwys correct b < 0 => b is negative integer.

Coming to Option [2] which states x< - b is not true ( as per my understanding)

Option [3] x>b is alwys true as we know that b Will alwys be negative

Plz guide

Posted from my mobile device

Hi

When we say b is negative, remember that the NEGATIVE sign is already included in b. The moment you add another negative, say -b, the - sign will get multiplied by the negative sign in b and make it positive.
Example.
Say b=-2, then -b=-(-2)=2=|2|
b=-2=-|2|