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The solution set of an inequality (a + b)x + 2a - 3b < 0

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The solution set of an inequality (a + b)x + 2a - 3b < 0

by Max@Math Revolution » Mon Dec 23, 2019 11:10 pm
[GMAT math practice question]

The solution set of an inequality (a + b)x + 2a - 3b < 0 is x < -1/3. What is the solution set of the inequality (a - 3b)x + b - 2a > 0, in terms of x?

A. x < -3
B. -3 < x < 3
C. -1 < x < 0
D. -1 < x < 3
E. 0 < x < 4
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by Max@Math Revolution » Thu Dec 26, 2019 2:31 am
=>

(a + b)x + 2a - 3b < 0
=> (a + b)x < 3b - 2a
=> x < (3b - 2a) / (a + b) under the assumption a + b > 0
Since its solution set is x < -(1/3), we have (3b - 2a) / (a + b) = -(1/3) or (-3)(3b - 2a) = a + b. Then we have 6a - 9b = a + b or a = 2b.
Since a = 2b, the inequality (a - 3b)x + b - 2a > 0 is equivalent to (2b - 3b)x + b - 4b > 0 or -bx - 3b > 0.
Then we have bx < -3b or x < -3.

Therefore, A is the answer.
Answer: A
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