Question

The numerator of a fraction is $6x+1$, the denominator is $7-4x$, and $x$ can have any value between $-2$ and $2$, both included. The values of $x$ for which the numerator is greater than the denominator are

• A. $\frac{3}{5}<x\le 2$
• B. $\frac{3}{5}\le x\le 2$
• C. $0<x\le 2$
• D. $0\le x\le 2$
• E. $-2\le x\le 2$

Answer 1

The correct option is A $\frac{3}{5}<x\le 2$

Given :

Numerator: $6x+1$

denominator : $7-.4x$

and $-2\le x\le \mathrm{2................}\left(i\right)$

according to question

$\Rightarrow 6x+1>7-4x$

$\Rightarrow 10x+1>7$

$\Rightarrow 10x>6$

$\Rightarrow x>\frac{6}{10}$

$\Rightarrow x>\frac{3}{5}...........\left(ii\right)$

from $\left(i\right)and\left(ii\right)$

$=\frac{3}{5}<x\le 2$

$\text{Option A is correct.}$