Question

Solve the given inequality for real x:
$\frac{x}{4}<\frac{(5x-2)}{3}-\frac{(7x-3)}{5}$

Answer 1

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

$\Rightarrow \frac{x}{4}<\frac{5x}{3}-\frac{2}{3}-\frac{7x}{5}+\frac{3}{5}$

$\Rightarrow \frac{x}{4}-\frac{5x}{3}+\frac{7x}{5}<\frac{-2}{3}+\frac{3}{5}$

$\Rightarrow \frac{15x-100x+84x}{60}<\frac{-10+9}{15}$

$\Rightarrow \frac{-x}{60}<\frac{-1}{15}$

Multiplying both sides by 60, we have

$-x<-4$

Dividing both sides by -1, we have

$x>4$

Thus the solution set is $(4,\infty )$.