Question

Solve the following inequality for the value(s) of $x$.

$\frac{2x-3}{4}+8\ge 2+\frac{4x}{3}$

• A. $x\le 6.3$
  
• B. $x\ge 6.3$
  
• C. $x\ne 6.3$
  
• D. Data Insufficient

Answer 1

The correct option is A $x\le 6.3$

Given, $\frac{2x-3}{4}+8\ge 2+\frac{4x}{3}$

$\Rightarrow \frac{2x-3}{4}+6\ge \frac{4x}{3}$

$\Rightarrow \frac{2x-3+24}{4}\ge \frac{4x}{3}$
$\Rightarrow \frac{2x+21}{4}\ge \frac{4x}{3}$

On cross-multiplying, we get
$\Rightarrow 6x+63\ge 16x$
$\Rightarrow 10x\le 63$
$\Rightarrow x\le 6.3$

Hence, option A is correct.