Question

Which of the following is the solution set of the inequality $\frac{x}{4}<\frac{(5x-2)}{3}-\frac{(7x-3)}{5}$ ?

• A. $(4,\infty )$
• B. $(-\infty ,4)$
• C. $[4,\infty )$
• D. $(-\infty ,4]$

Answer 1

Answer: (A)

We have, $\frac{x}{4}<\frac{(5x-2)}{3}-\frac{(7x-3)}{5}$
$\frac{x}{4}<\frac{5(5x-2)-3(7x-3)}{15}$
$\Rightarrow 15x<4[(25x-10)-(21x-9)]$
$\Rightarrow 15x<4[(25x-10-21x+9]$
$\Rightarrow 15x<4[4x-1]$
$\Rightarrow 15x<16x-4$
Transferring the term $16x$ to $LHS$.
$15x-16x<-4\Rightarrow -x<-4$
Multiplying by $-1$ both sides, we get