This kind of work is easy to self check. Remember they are inequalities and not equations.
1) x^2 + x -2 > 0
....do I just factor then that what x can not be?
x=-2 or x=1
In this example x equals neither -2 nor 1 but if you plug in a value of x to the left or right of those values say x = -3 you will be able to tell where the less than and greater than signs go.
(-3)^2 +(-3) -2 = 4> 0 is true so it is safe to say that the region to the left of x=-2 is true for all values and by default (but you can check) region to the right of x=1 will also be true for this equality.
Hence x<-2 and x>1 satisfies this inequality.
You are right to treat them all as equations to get the critical values of x however.