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Question

Solve the following inequality:
$$\displaystyle\, \left ( \dfrac{1}{5} \right )^\frac{2x + 1}{1 - x} > \left ( \frac{1}{5} \right )^{-3}$$


Solution

$${ (\cfrac { 1 }{ 5 } ) }^{ \cfrac { 2x+1 }{ 1-x }  }>{ (\cfrac { 1 }{ 5 } ) }^{ -3 }$$
$$ { (5 })^{ \cfrac { 2x+1 }{ x-1 }  }>{ 5 }^{ 3 }$$
$$ \cfrac { 2x+1 }{ x-1 } >3$$
$$ \cfrac { 2x+1-3(x-1) }{ x-1 } >0$$
$$ \cfrac { 2x+1-3x+3 }{ x-1 } >0$$
$$ \cfrac { 4-x }{ x-1 } >0$$
$$ \cfrac { x-4 }{ x-1 } <0$$
$$ x\quad \varepsilon (1,4)$$

Maths

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