If |3 x|

Question

If |3 – x| < x + 5, which of the following may be true about x ?
 
I. x > –1
II. x < 2
III. x < –2

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

chetan2u · Answer

|3 – x| < x + 5 Two case: (1) 3-x>0 or x<3 : 3-x-2…….x>-1, so I and II will fit in. (2) 3-x\leq 0 or x>3 : x-3-1. Only I and II. C Bunuel , Typo in OA, I am correcting it.

Sahil2208 · Answer

chetan2u 
How II is valid? Since x > -1, what if x = -5? Still x < 2. Please help if I'm missing somewhere

chetan2u · Answer

Hi

The question is MAY be true and not MUST be true, so any small value fitting in that range is sufficient.

Now we know values between -1 and 2 are valid for range x<2.

For that matter even x<-0.99 MAY be true as -0.995 or -0.998 or -0.999 will give an answer yes to expression.

Kinshook · Answer

Asked: If |3 – x| < x + 5, which of the following may be true about x ?

|3 – x| < x + 5
Case 1: x>=3
x-3 < x+5
-3 < 5
ALWAYS TRUE

Case 2: x<3
3-x < x+5
x > -1
-1 <x < 3

Combining x>=3 and -1<x<3
x > -1

I. x > –1: ALWAYS TRUE
II. x < 2: MAY BE TRUE
III. x < –2: CAN NOT BE TRUE

IMO C

Purnank · Answer

In such question,
Please put nearby values from given option and check.
you will notice only I and II these two are valid. for may be true condition.

BrushMyQuant · Answer

|3 – x| < x + 5
=> | x - 3 | < x + 5

We have two cases as we have one modulus
-Case 1: x - 3 ≥ 0 => \| x - 3 \| = x - 3 => x - 3 < x + 5 => 8 > 0 Which is true always => x - 3 ≥ 0 is a solution => x ≥ 3 is TRUE	-Case 2: x - 3 ≤ 0 => \| x - 3 \| = -(x - 3) => - (x - 3) < x + 5 => -x + 3 < x + 5 => 2x > -2 => x > -1 BUT the range was x ≤ 3 => -1 < x ≤ 3 is a solution

Combining both the solutions we get
-1 < x ≤ 3 and 3 ≤ x
=> -1 < x

I. x > –1
WILL BE TRUE ALWAYS

II. x < 2
MAY be TRUE for values of x between -1 and 2

III. x < –2
WILL NEVER BE TRUE as x > -1

So, Answer will be C
Hope it helps!

Watch the following video to MASTER Absolute Values

impeditrem · Answer

3 - x < x + 5

3 - 5 < x + x
-2 < 2x
-1 < x
x > -1

The question asks which of the following may be true (i.e., which statements describe a range that overlaps with our solution x > -1

I. x > -1: This is the exact solution. Since all values of x satisfy this, it definitely "may be true."
II. x < 2: Values like x = 0 or x = 1 are in our solution set (x > -1) and also satisfy x < 2. Therefore, this "may be true."
III. x < -2: Our solution requires x to be greater than -1. There is no overlap between x > -1 and x < -2. Therefore, this cannot be true.

Conclusion
Statements I and II can be true.

If |3 x| < x + 5, which of the following may be true about x ?

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