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18 May 2018, 01:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (02:07) correct
20%
(02:20)
wrong
based on 657
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Not Attempted Yet
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
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
18 May 2018, 01:44
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Solution
To find:
• The value of the inequality |8 – 2x| < 3y – 9 is equal to which of the options given
Approach and Working:
In general terms, we know if |x| < a, then -a < x < a
• Applying the same concept here, we can write,
- |8 – 2x| < 3y – 9
Or, -3y + 9 < 8 – 2x < 3y – 9
Or, 3y – 9 > 2x – 8 > 9 – 3y
Or, 3y – 1 > 2x > 17 – 3y
Hence, the correct answer is option E.
Answer: E
General Discussion
18 May 2018, 14:36
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Bunuel
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
All answer choices except B have \(2x\) isolated. Isolate 2x.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
\(|8 - 2x| < 3y - 9\)
Split the cases - solve simultaneously
\(-(3y - 9) < 8 - 2x < 3y - 9\)
\(-3y + 9 < 8 - 2x < 3y - 9\)
Subtract \(8\)
\(-3y + 1 < -2x < 3y - 17\)
Divide by \((-1)\)
\(3y - 1 > 2x > -3y + 17\)
\(=\)
\(3y - 1 > 2x > 17 - 3y\)
Answer E
Split the cases - solve separately
This way might be easier for some.
CASE 1:
\(8 - 2x < 3y - 9\)
\(-2x < 3y -17\)
Divide by \(-1\)
\(2x > -3y + 17\)
\(2x > 17 - 3y\)
CASE 2:
\(8 - 2x > -(3y - 9)\)
\(8 - 2x > -3y + 9\)
\(-2x > -3y + 1\)
Divide by \(-1\)
\(2x < 3y - 1\), OR
\(3y - 1 > 2x\)
Combine: \(3y - 1 > 2x > 17 - 3y\)
Answer E
