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
I'm confused how to set up the formulas here. Can any experts help?
OA B
Which of the following inequalities
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|x-y| = the DISTANCE between x and ylheiannie07 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
The midpoint between -2 and 4 = the average of -2 and 4 = (-2+4)/2 = 1.
-2 < x < 4 implies that x can be any value between -2 (3 places to the LEFT of 1) and 4 (3 places to the RIGHT of 1).
In other words: the distance between x and 1 must be less than 3.
In math terms:
|x-1| < 3.
The correct answer is B.
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https://www.beatthegmat.com/inequalities-t299234.html
https://www.beatthegmat.com/absolute-val ... 74256.html
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We know that, if |something| < b (when b is positive), then -b < something < blheiannie07 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
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
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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
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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
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Rich
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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: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
|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
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