Question

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

• A. (-$\infty$,3)
• B. (1,3)
• C. (4,$\infty$)
• D. ( - $\infty$ ,- l)
• E. (3,4)

Answer 1

Answer: (C)

Given,
$x+7<\,2 x+3$
$\Rightarrow \, 4 \leq x$
$ \Rightarrow x>\,4\,\,\,\,\,\,\,\dots(i)$
and $2 x+4<\,5 x+3$
$\Rightarrow \, 1<\,3 $
$ \Rightarrow x >\,\frac{1}{3}\,\,\,\,\,\,\dots(ii)$
From Eqs. (i) and (ii), we get the common interval $(4, \infty)$ i.e., $x \in(4, \infty)$