The set of values of x which satisfy $5\mathrm{x}+2<3\mathrm{x}+8 \mathrm{and} \frac{\mathrm{x}+2}{\mathrm{x}-1}<4, \mathrm{is}$

$\mathrm{Given} \mathrm{that} : 5\mathrm{x}+2<3\mathrm{x}+8 \mathrm{and} \frac{\mathrm{x}+2}{\mathrm{x}-1}<4,$

$\Rightarrow 5x-3x<8-2 and \frac{x+2}{x-1}-4<0$

$\Rightarrow 2x<6 and \frac{x+2-4x+4}{x-1}<0$

$\Rightarrow x<3 and \frac{-3(x-2)}{x-1}<0$

$\Rightarrow x<3 and \frac{x-2}{x-1}>0$

So , we can see that all the values of x lying in $(-\infty , 1)\cup (2,3)$ satisfy the equations and no other value outside the interval satisfy it.