Question

write the set of values of x satisfying the inequations 5x+2<3x+8 and $\frac{x+2}{x-1}<4$.

Answer 1

$5x+2<3x+8\Rightarrow 2x<6\Rightarrow x<3\therefore \text{Solution set for inequation~(i)~is}(-\infty ,3)\frac{x+2}{x-1}<4\Rightarrow \frac{x+2}{x-1}-4<0\Rightarrow \frac{x+2-4x+4}{x-1}<0\Rightarrow \frac{-3x+6}{x-1}<0\Rightarrow \frac{x-2}{x-1}>0\text{Solution set for inequation (ii) is}\therefore (-\infty ,1)\cup (2,\infty )\text{Hence,the solution set for the given system of inequation is}(-\infty ,1)\cup (2,3)$