Question

Solve the inequality for real $x$.

$\frac{x}{4}<\frac{(5x-2)}{3}-\frac{(7x-3)}{5}$

Answer 1

Given, $\frac{x}{4}<\frac{(5x-2)}{3}-\frac{(7x-3)}{5}$

$\Rightarrow \frac{x}{4}<\frac{5(5x-2)-3(7x-3)}{15}$

$\Rightarrow \frac{x}{4}<\frac{(25x-10-21x+9)}{15}$

$\Rightarrow \frac{x}{4}<\frac{4x-1}{15}$

$\Rightarrow 15x<4(4x-1)$

$\Rightarrow 15x<16x-4$

$\Rightarrow 4<16x-15x$

$\Rightarrow x>4\text{or}x\in (4,\infty )$