Solve 2^{|x+2|}-|2^{x+1}-1|=2^{x+1}+1

[utkarshakash]

Homework Statement

$2^{|x+2|}-|2^{x+1}-1|=2^{x+1}+1$

Homework Equations

The Attempt at a Solution

I know this is not a direct equation in quadratic but somehow I have to convert it in that form by assuming something to be another variable. I am supposing $2^x=t$. But that doesn't help me as I cannot eliminate $2^{|x+2|}$

 

[HallsofIvy]

The first thing I would do it set up "cases" to handle the absolute values. x+ 2 will be positive for x> -2 and $2^{x+ 1}- 1> 0$ for x> -1. So if x< -2, both x+ 2 and $2^{x+1}-1$ are negative. If -2< x< -1, x+ 2 is positive but $2^{x+1}- 1$ is still negative. If x> -1, both x+ 2 and $2^{x+1}- 1$ are positive.

Also use the fact that $2^{x+ a}= 2^a 2^x$.