Which of the following inequalities

lheiannie07 wrote: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

We know that, if |something| < b (when b is positive), then -b < something < b
For example, if |2x+1| < 5 , then -b < 2x+1 < 5

We're going to apply the above rule IN REVERSE

Given: –2 < x < 4
Subtract 1 from all parts: -3 < x-1 < 3
So: |x-1| < 3

Answer: B

Cheers,
Brent

Hi lheiannie07,

We're asked which of the following inequalities is equivalent to -2 < X < 4. This question can be solved with a bit of 'brute force' and TESTing VALUES.

To start, let's see what happens to each answer when X approaches its MAXIMUM value (re: X gets really close to 4).

Answer A): |X - 2| < 4
Here, as X gets close to 4, |X - 2| gets really close to 2.... but that's not 'close' to the '4' in this inequality. Eliminate Answer A.

Answer B: |X - 1| < 3
Here, as X gets close to 4, |X - 1| gets really close to 3.... which is a match for this inequality. Keep Answer B for now.

Answer C: |X + 1| < 3
Here, as X gets close to 4, |X + 1| gets really close to 5.... but that's greater than the '4' in this inequality. Eliminate Answer C.

Answer D: |X + 2| < 4
Here, as X gets close to 4, |X + 2| gets really close to 6.... but that's greater than the '4' in this inequality. Eliminate Answer D.

At this point, the Answer is either B or E. Let's check see what happens to Answer B as X approaches its MINIMUM value (re: X gets really close to -2).

Answer B: |X - 1| < 3
Here, as X gets close to -2, |X - 1| gets really close to 3.... which is a match for this inequality. Answer B matches the range given by the initial inequality, so it MUST be the answer.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

lheiannie07 wrote: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

We need to go through the inequalities in the answer choices by solving them without the absolute value sign. However, at first glance, we can eliminate choices A and D since there is no way we can still have the 4 on the right hand side of the final answer when we solve the inequality without the absolute value sign (for example, x - 2 < 4 will become x < 6). So let’s look at choice B first:

|x - 1| < 3 means x - 1 < 3 or -(x - 1) < 3.

If x - 1 < 3, then x < 4.

If -(x - 1) < 3, then x - 1 > -3 or x > -2.

Therefore, we have -2 < x < 4.

Answer: B