Question

Solve the following inequation and write the solution set :
$13x-5<15x+4<7x+12,x\in R$
Represent the solution on a real number line.

Answer 1

Given : $13x-5<15x+4<7x+12$
$\Rightarrow$ $15x+4>13x-5$ and $15x+4<7x+12$
$\Rightarrow$ $15x-13x>-5-4\Rightarrow 15x-7x<12-4$
$\Rightarrow$ $2x>-9\Rightarrow 8x<8$
$\Rightarrow$ $x>\frac{-9}{2}\Rightarrow x<1$
Solution : $\{x:\frac{-9}{2}<x<1,x\in R\}$