Solve the equation
`2^(|x+1|)-2^(x)=|2^(x)-1|+1`

Explanation

Find the critical points:brgt
`x+1=0, 2^(x)-1=0`
`:.x=-1,x=0`
Now consider the following cases,
`x lt-1`
`2^(-(x+1))-2^(x)=-(2^(x)-1)+1`
`implies2^(-(x+1))=2`
`:.-(x+1)=1`
`:.x=-2`..i
`-1lexlt0` ltbr `2^(x+1)-2^(x)=-(2^(x)-1)+1`
`implies2^(x+1)=2`
`:.x+1=1`
`:.x=0`
`x!=[ :' -1lexlt0]`
`xge0`
`2^(x+1)-2^(x)=2^(x)-1+1`
`implies2^(x+1)=2.2^(x)`
`implies2^(x+1)=2^(x+1)`
which is true for `xge0`..............ii
Now, combining all cases we have the final solution as
`x epsilon [0,oo)uu{-2}`