Solutions of an exponential equation from two graphs

This question is about the equation \(2^x=x+2\).

1. Verify that \(x=2\) is a solution.[1]
2. By evaluating \(2^x-x-2\) at \(x=-2\) and at \(x=-1\), show that there is another solution \(\alpha\) with \(-2<\alpha<-1\).[2]
3. Sketch \(y=2^x\) and \(y=x+2\) on the same axes, and explain why the equation has exactly two solutions.[2]
4. Given that \(\alpha\approx-1.69\), state the set of values of \(x\) for which \(2^x<x+2\).[2]