The set of values of x satisfying the system of inequalities $5x + 2 < 3x+8$ and $\frac{x+2}{x-1}<4$ is
Answer & explanation
Correct answer: option 4
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 $x ∈(-∞, 1) ∪ (2,∞)$
$⇒x∈(-∞, 1) ∪ (2, 3)$