Question

​Solve the following system of equations
​(i) 2x+1/7x-1>5, x+7/x-8>2

Answer 1

Dear student,

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \frac{2\mathrm{x}+1}{7\mathrm{x}-1}>5 \\ \Rightarrow 2\mathrm{x}+1>35\mathrm{x}-5 \\ \Rightarrow 35\mathrm{x}-2\mathrm{x}<1+5 \\ \Rightarrow 33\mathrm{x}<6 \\ \Rightarrow \mathrm{x}<\frac{6}{33} \\ \Rightarrow \mathrm{x}<\frac{3}{11} \\ \mathrm{Also}, \\ \frac{\mathrm{x}+7}{\mathrm{x}-8}>2 \\ \Rightarrow \mathrm{x}+7>2\mathrm{x}-16 \\ \Rightarrow 2\mathrm{x}-\mathrm{x}<7+16 \\ \Rightarrow \mathrm{x}<23 \\ \mathrm{So},\mathrm{x}<\frac{3}{11} \end{gathered}$$

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