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Question

Solve the system of inequalities: x+7x8>2,2x+17x1>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+7x8>2
x+7x82>0
x+72x+16x8>0
x+23x8>0
x23x8<0 (a<b=>a>b)
Values of x satisfying this inequality are:
x(8,23)
Now:
2x+17x1>5
2x+17x15>0
2x+135x+57x1>0
33x+67x1>0
11x27x1<0 (a<b=>a>b)
x211x17<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.

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