Question

The range of values of $x$ which satisfy $5x+2<3x+8$ and $\frac{x+2}{x-1}<4$ are

• A. $(2,3)$
• B. $(-\infty ,1)\cup (2,3)$
• C. $(2,\infty )$
• D. $R$

Answer 1

The correct option is B $(-\infty ,1)\cup (2,3)$

$5x+2<3x+82x<6x<3$
Now, the second inequality is $\frac{(x+2)}{(x-1)}<4$
The expression can be written as $1+\frac{3}{x-1}<4$
$3/(x-1)<3$
$1/(x-1)<1$
$x>2$ or $x<1$
$\therefore$ Option B.