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&gt; 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.