Question

Find the value of $x$ in $\frac{10}{2x}-\frac{4}{2x}\ge \frac{24}{2}\times \frac{3}{4}$ if $x$ is a positive number.

• A. $x\le \frac{1}{3}$
  
• B. $\frac{1}{3}\le x$
  
• C. $3\ge x$
  
• D. $3\le x$
  

Answer 1

The correct option is A $x\le \frac{1}{3}$


Given, $\frac{10}{2x}-\frac{4}{2x}\ge \frac{24}{2}\times \frac{3}{4}$.

Simplify the equation to it's full capacity.
$\frac{10}{2x}-\frac{4}{2x}\ge 9$ [$\because \frac{24\times 3}{2\times 4}=\frac{72}{8}=9$ ]

Since the denominator is same (i.e. $2x$), the LCM would be $2x$.

$\Rightarrow \frac{10-4}{2x}\ge 9$

$\Rightarrow \frac{6}{2x}\ge 9$

$\therefore$ Multiplying both sides with $2x$ will not change the sign of inequality because $x$ is a positive number. Hence, $2x$ is also a positive number.

$\frac{6}{2x}\times 2x\ge 9\times 2x$

$6\ge 18x$

$\to$Transfer 18 to L.H.S

$\frac{6}{18}\ge x$

$\frac{1}{3}\ge x$ which can also be written as $x\le \frac{1}{3}$

Hence, option (a.) is the correct choice