The set of values of x satisfying the system of inequalities $5x + 2 < 3x+8$ and $\frac{x+2}{x-1}<4$ is

(-∞, 1) ∪ (2, 3)

We have,

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

$⇒2x-6<0$ and $\frac{x+2}{x-1}-4<0$

$⇒2(x-3) <0$ and $\frac{-3x+6}{x-1}<0$

$⇒x-3<0$ and $\frac{x-2}{x-1}>0$

$⇒x∈ (-∞, 3)$ and $x ∈(-∞, 1) ∪ (2,∞)$

$⇒x∈(-∞, 1) ∪ (2, 3)$