If |x + 1| 2x 1, which of the following represents the correct

Question

If |x + 1| > 2x – 1, which of the following represents the correct range of values of x ?

A. x < 0
B. x < 2
C. –2 < x < 0
D. –1 < x < 2
E. 0 < x < 2

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Adit_ · Answer

Option B  perfectly fits the equation as stated.

vasu1104 · Answer

case 1: x+1 > 2x-1 -x > -2 x<2 case 2: -x-1 > 2x-1 0>-3x 3x<0 x<0 only option B covers the correct range of values of X

BongBideshini · Answer

|x + 1| > 2x − 1 Case 1: x ≥ −1 x + 1 > 2x − 1 2 > x x < 2 From this case: −1 ≤ x < 2 Case 2: x < −1 −x − 1 > 2x − 1 −3x > 0 x < 0 Since this case already requires x < −1, all such values satisfy it. From this case: x < −1 Combine both cases: x < −1 and −1 ≤ x < 2 => x < 2 Answer: B

ExpertsGlobal5 · Answer

B is the correct answer choice.

Video explanation:

https://www.youtube.com/watch?v=wkdUHNh37GI

doloribusnobis · Answer

CAN SOMEONE PLEASE EXPLAIN WHY OPTION D IS NOT THE ANSWER? |x + 1| > 2x − 1 Case 1: x ≥ −1 x + 1 > 2x − 1 2 > x x < 2 From this case: −1 ≤ x < 2 AS THE INEQUALITY IS DEFINED ONLY FROM THE RANGE OPTION D: -1 < x < 2.

Bunuel · Answer

Your mistake is throwing out Case 2. In that case, you already assume x < -1, and the inequality simplifies to x < 0, which is automatically true for every x < -1, so all values x < -1 are valid. Combining that with Case 1, -1 ≤ x < 2, gives x < 2.

Alternatively, you can think about it this way. If x is negative, then the right-hand side, 2x - 1, is negative. But the left-hand side, |x + 1|, is always nonnegative. Therefore, the left-hand side must be greater than the right-hand side for every negative value of x, so all negative x satisfy the inequality.

If |x + 1| > 2x 1, which of the following represents the correct

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