If |3 x|

Question

If |3 – x| < x + 5, which of the following may be true about x?
 
I. x < 0
II. x < –1
III. x > 2

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

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dp1234 · Answer

Solved using putting in values, since question asks "may be true", choose values to satisfy the inequality, x= -0.5 , |3-(-0.5)| < -0.5+5 => 3.5 <4.5. Thus (1) may be true. x = -1, |3-(-1)|< -1+5 => 4 < 4. Clearly any value less than -1 will not hold true for inequality. (2) not true. x= 3. |3-3| < 3+5 which is true. So (3) is true. Solution - D

chloreton · Answer

|3 – x| < x + 5 Case 1: When 3-x >=0 ie, x<=3 3-x < x+5 -2 < 2x x>-1 Therefore for x<=3, the range is -13 -(x-3) < x+5 We can see x gets cancelled out. Discard. Therefore, the overall range is -1

thisisakr · Answer

Solving the inequality |3 - x| < x + 5.
First, note that for the inequality to hold, x + 5 must be positive, so x > -5.
Case 1: 3 - x ≥ 0, meaning x ≤ 3
3 - x < x + 5, giving -2 < 2x, so x > -1.
Combined with x ≤ 3, this gives -1 < x ≤ 3.
Case 2: 3 - x < 0, meaning x > 3
-(3 - x) < x + 5, giving x - 3 < x + 5, giving -3 < 5, which is always true.
Combined with x > 3, this gives x > 3.
Overall solution: x > -1
Now checking the three statements:
Statement I: x < 0. This is possible since x can be any value between -1 and 0, for example x = -0.5. This MAY be true.
Statement II: x < -1. This is never true since the solution requires x > -1. This cannot be true.
Statement III: x > 2. This is possible since x can be greater than 2. This MAY be true.
The answer is D — I and III only.

BongBideshini · Answer

|3 − x| < x + 5 Case 1: 3 − x ≥ 0 → x ≤ 3 Then: 3 − x < x + 5 → 3 - x < x + 5 → -2 < 2x → x > -1 So from this case: -1 < x ≤ 3 Case 2: 3 − x < 0 → x > 3 Then: |3 − x| = x − 3 x − 3 < x + 5 → always true So: x > 3 Combine both: x > -1 Now check statements: I. x < 0 → possible (e.g., x = -0.5) II. x < -1 → not possible III. x > 2 → possible (e.g., x = 3) Ans: D. (I and III only)

ExpertsGlobal5 · Answer

D is the correct answer choice.

Video Explanation:

https://www.youtube.com/watch?v=Cq6FqI5isr8

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

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