Q. Which of the following is the solution set of the inequality $\frac{x}{4}<\frac{(5 x-2)}{3}-\frac{(7 x-3)}{5}$ ?
Linear Inequalities
Solution:
We have, $\frac{x}{4}<\frac{(5 x-2)}{3}-\frac{(7 x-3)}{5} $
$\frac{x}{4}<\frac{5(5 x-2)-3(7 x-3)}{15} $
$ \Rightarrow 15 x<4[(25 x-10)-(21 x-9)] $
$ \Rightarrow 15 x<4[(25 x-10-21 x+9] $
$\Rightarrow 15 x<4[4 x-1] $
$ \Rightarrow 15 x<16 x-4$
Transferring the term $16 x$ to $LHS$.
$15 x-16 x< -4 \Rightarrow-x<-4$
Multiplying by $-1$ both sides, we get
