Solve the system of inequalities: x+7x−8>2,2x+17x−1>5.
A
(−16/7,5/7)
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B
(−7/8,2/7)
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C
(2,5)
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D
No solution
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Solution
The correct option is D No solution x+7x−8>2 x+7x−8−2>0 x+7−2x+16x−8>0 −x+23x−8>0 x−23x−8<0(a<b=>−a>−b) Values of x satisfying this inequality are: x∈(8,23) Now: 2x+17x−1>5 2x+17x−1−5>0 2x+1−35x+57x−1>0 −33x+67x−1>0 11x−27x−1<0(a<b=>−a>−b) x−211x−17<0 Values of x satisfying this inequality are: x∈(17,211) We can see from the solution sets that no value of x satisfy both the inequality.