I suspect that the problem should read as follows:
If (x²-6x+8)/(3x²+14x+16) < 0, then the solution set for the inequality is:
a. -8/3<x<4
b. -8/3<x<-2 or 2<x<4
c. -2<x<4
d. x>4
e. 5<x<8
The answer choices offer possible ranges for x.
TEST EASY VALUES that are included in some ranges but not in others.
Test x=0 in (x²-6x+8)/(3x²+14x+16):
(0²- 6*0 + 8)/(3*0² + 14*0 + 16) = 8/16 = 1/2.
Since the result is not negative, x=0 is not a valid solution.
Since x=0 is included in the ranges for A and C, eliminate A and C.
Test x=6 in (x²-6x+8)/(3x²+14x+16):
(6²- 6*6 + 8)/(3*6² + 14*6 + 16) = 8/(positive) = positive.
Since the result is not negative, x=6 is not a valid solution.
Since x=6 is included in the ranges for D and E, eliminate D and E.
The correct answer is
B.
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