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