Solve the following system of equations in R. 4 x+1 3 6 x+1 ,x>0 - Vidyadip

Question

Solve the following system of equations in R. $\frac{4}{\text{x}+1}\leq3\leq\frac{6}{\text{x}+1},\text{x}>0$

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Answer

Consider the first inequation, $\frac{4}{\text{x}+1}\leq3\leq\frac{6}{\text{x}+1}$ $\Rightarrow4\leq3(\text{x}+1)\leq6$ $\Rightarrow\frac{4}{3}\leq(\text{x}+1)\leq6$ $\Rightarrow\frac{4}{3}-1\leq\text{x}\leq2-1$ $\Rightarrow\frac{1}{3}\leq\text{x}\leq1$ Solution set for given inequation is $\Big[\frac{1}{3},1\Big].$

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