Question

Solve the inequality and show the graph of the solution on number line:

$\frac{x}{2}\ge \frac{(5x-2)}{3}-\frac{(7x-3)}{5}$

Answer 1

Given, $\frac{x}{2}\ge \frac{(5x-2)}{3}-\frac{(7x-3)}{5}$
$\Rightarrow \frac{x}{2}\ge \frac{5(5x-2)-3(7x-3)}{15}$
$\Rightarrow \frac{x}{2}\ge \frac{25x-10-21x+9}{15}$
$\Rightarrow \frac{x}{2}\ge \frac{4x-1}{15}$
$\Rightarrow 15x\ge 2(4x-1)$
$\Rightarrow 15x\ge 8x-2$
$\Rightarrow 7x\ge -2$

$\Rightarrow x\ge -\frac{2}{7}$