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The inequality
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17 Sep 2017, 03:59
17 Sep 2017, 03:59
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Question Stats:
83% (02:16) correct
16% (02:41) wrong based on 80 sessions
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The inequality |8 - 2x| < 3y - 9 is equivalent to which of the following?
A. \(2x < \frac{(17 - 3Y)}{2}\)
B. 3y + 2x > 1
C. 6y – 2 < 2x
D. 1 – y < 2x < 17 + y
E. 3y – 1 > 2x > 17 – 3y
Re: The inequality
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18 Sep 2017, 00:10
18 Sep 2017, 00:10
1
|8-2x| is equal to 8-2x when 8-2x >=0 and equal to 2x-8 when 8-2x<0. Thus, we can rewrite the disequality as two, i.e. 8-2x<3y-9 and 2x-8<3y-9. Rearranging and having looked at the answer choices, it is meaningful to explicit the term 2x as 2x>17-3y from the first disequality and 2x<3y-1 from the second one. This can be rewritten as 3y-1>2x>3y-17. Thus, the answer is E!
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Re: The inequality
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31 Dec 2021, 02:41
31 Dec 2021, 02:41
2
Given that |8 - 2x| < 3y - 9
Now, we know that |x| < a => -a < x < a (Watch this video to learn about the Basics of Absolute Value)
=> |8 - 2x| < 3y - 9
=> -(3y - 9) < 8-2x < 3y - 9
Multiplying all the sides by -1 we get
3y-9 > 2x-8 > 9-3y
=> 9-3y < 2x-8 < 3y-9
Adding 8 on all the sides we get
=> 9-3y+8< 2x-8 + 8< 3y-9 + 8
=> 17-3y < 2x < 3y - 1
=> 3y – 1 > 2x > 17 – 3y
So, Answer will be E
Hope it helps!
Watch the following video to learn How to Solve Absolute Value Problems
Now, we know that |x| < a => -a < x < a (Watch this video to learn about the Basics of Absolute Value)
=> |8 - 2x| < 3y - 9
=> -(3y - 9) < 8-2x < 3y - 9
Multiplying all the sides by -1 we get
3y-9 > 2x-8 > 9-3y
=> 9-3y < 2x-8 < 3y-9
Adding 8 on all the sides we get
=> 9-3y+8< 2x-8 + 8< 3y-9 + 8
=> 17-3y < 2x < 3y - 1
=> 3y – 1 > 2x > 17 – 3y
So, Answer will be E
Hope it helps!
Watch the following video to learn How to Solve Absolute Value Problems
