Question

If $7x-2<4-3x$ and $3x-1<2+5x$, then $x$ lies in the interval

• A. $\left(\frac{3}{5},\frac{3}{2}\right)$
• B. $\left(\frac{-3}{2},\frac{3}{5}\right)$
• C. $\left[-\frac{3}{2},\frac{3}{5}\right)$
• D. $\left[-\frac{3}{2},\frac{3}{5}\right]$
• E. $\left(-\frac{3}{5},\frac{3}{2}\right)$

Answer 1

Answer: (B)

Given, $7x-2<4-3x$ and $3x-1<2+5x$
$\therefore 7x+3x<4+2$
and $3x-5x<2+1$
$\Rightarrow 10x<6$ and $-2x<3$
$\Rightarrow x<\frac{3}{5}$ and $x>-\frac{3}{2}$
$\therefore x\in \left(-\frac{3}{2},\frac{3}{5}\right)$