The other tutor's solution is incorrect. It should be

There's one of your errors! -1 times A + 2 is -1(A + 2) and then you
use the distributive principle to remove the parentheses, and
you end up with -A - 2, (not A + 2).

But also when you multiply through by a variable quantity, A + 2, if that
quantity happens to be negative you would have to change the direction
of the inequality.  So 



would only become

 if  which is the same as 

But it would become

 if  which is the same as 

So two cases must be considered to which if either is valid of
if they both are:

Solving the first case

Case 1:

 if  or 

Add A to both sides:

 if 

 if 

Add 5 to both sides

 if 

 if  

Divide both side by 2

 if 

That gives us the solution set:



--------------------

Solving Case 2:

 if  or 

Add A to both sides:

 if 

 if 

Add 5 to both sides

 if 

 if  

Divide both side by 2

 if 

This is a contradiction, since A cannot be greater than 
and at the same time be less than or equal to -2, so the only solution
is given by case 1.



Edwin