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Which of the following represents the solution of |x-1|<2 ?
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06 Dec 2019, 10:58
06 Dec 2019, 10:58
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Which of the following represents the solution of \(|x-1|<2\) ?
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Re: Which of the following represents the solution of |x-1|<2 ?
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08 Dec 2019, 09:40
08 Dec 2019, 09:40
1
Carcass wrote:
Which of the following represents the solution of \(|x-1|<2\) ?
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#greprepclub Which of the following represents the solution.jpg
---------ASIDE------------
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
----------------------------------
GIVEN: \(|x-1|<2\)
Apply Rule #1 to get: \(-2 < x - 1 < 2\)
Add 1 to all sides to get: \(-1 < x < 3\)
Answer: A
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Brent
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Re: Which of the following represents the solution of |x-1|<2 ?
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23 Dec 2021, 09:49
23 Dec 2021, 09:49
1
We need to find the solution range for the inequality \(|x-1|<2\)
We can open the Absolute value by taking two cases
Case 1: x-1 >= 0
=> |x-1| = x-1 (Check this video to know how to deal with Absolute Value problems)
=> x - 1 < 2
=> x < 2 + 1
=> x < 3 ... (1)
Case 2: x-1 < 0
=> |x-1| = -(x-1) = -x + 1 (Check this video to know how to deal with Absolute Value problems)
=> -x + 1 < 2
=> x > 1 - 2
=> x > -1 ...(2)
Combining (1) and (2) we get (Check this video to know how to merge Inequalities)
x > -1 and x < 3
=> -1 < x < 3
So, we will have a line segment connecting -1 to 3 and there will be two empty circles at -1 and 3 indicating that -1 and 3 are not included in the solution.
So, Answer will be A
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
We can open the Absolute value by taking two cases
Case 1: x-1 >= 0
=> |x-1| = x-1 (Check this video to know how to deal with Absolute Value problems)
=> x - 1 < 2
=> x < 2 + 1
=> x < 3 ... (1)
Case 2: x-1 < 0
=> |x-1| = -(x-1) = -x + 1 (Check this video to know how to deal with Absolute Value problems)
=> -x + 1 < 2
=> x > 1 - 2
=> x > -1 ...(2)
Combining (1) and (2) we get (Check this video to know how to merge Inequalities)
x > -1 and x < 3
=> -1 < x < 3
So, we will have a line segment connecting -1 to 3 and there will be two empty circles at -1 and 3 indicating that -1 and 3 are not included in the solution.
So, Answer will be A
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
