Question

If $x+7<2x+3$ and $2x+4<5x+3$, then $x$ lies in the interval

• A. $(3,\infty )$
• B. $(1,3)$
• C. $(4,\infty )$
• D. $(\frac{1}{3},\infty )$

Answer 1

The correct option is C $(4,\infty )$

$\left(i\right)$ $x+7<2x+3$
$\Rightarrow x<2x+3-7$
$\Rightarrow x<2x-4$
$\Rightarrow -x<-4$
$\Rightarrow x>4...\left(1\right)$

$\left(ii\right)$ $2x+4<5x+3$
$\Rightarrow 2x<5x-1$
$\Rightarrow -3x<-1$
$\Rightarrow x>\frac{1}{3}...\left(2\right)$
From eqn$\left(1\right)$ and $\left(2\right),$ $x>4$