Question:
Solve each of the following in equations and represent the solution set on the number line.
$\frac{x}{4}<\frac{(5 x-2)}{3}-\frac{(7 x-3)}{5}$ where $x \in \mathbf{R}$.
Solution:
Given:
$\frac{x}{4}<\frac{(5 x-2)}{3}-\frac{(7 x-3)}{5}$, where $x \in R$
Multiplying 60 on both the sides in the above equation,
$\frac{x}{4}(60)<\frac{(5 x-2)}{3}(60)-\frac{(7 x-3)}{5}(60)$
$15 x<20(5 x-2)-12(7 x-3)$
$15 x<100 x-40-84 x+36$
$15 x<16 x-4$
Now, subtracting 16x from both sides in above equation
$15 x-16 x<16 x-4-16 x$
$-x<-4$
Now, multiplying by -1 on both sides in above equation
$(-x)(-1)<(-4)(-1)$
$x>4$ (inequality sign reversed)
