Question

Find the solution of the inequation $|2^x-1|+|4-2|\le 3$

Answer 1

$|2^x-1|+|4-2|\le 3$

$|2^x-1|+2\le 3$

$|2^x-1|\le 1$

$x\ge 0$

$\Rightarrow 2^x-1\le 1$

$2^x\le 2$

$x\le 1$

$\therefore xϵ[0,1]...\left(1\right)$

$x<0$

$\therefore 1-2^x\le 1$

$0\le 2^x$

$\Rightarrow xϵR$

$\therefore xϵ(-\infty ,0)...\left(2\right)$

$\therefore \left(1\right)\cup \left(2\right)\Rightarrow$

$xϵ(-\infty ,1)$ Ans