Inequalities help

I'm doing a question with inequalities which i initially thought was very simple...

"solve the inequality ((2x-5)/(x+1))<1"

I solved it as if < is a = and eventually got x<6 (which is correct) but there were additional workings to find -1<x which i dont get where that has come from??

In the workings they made the inequality into a quadratic inequality, which i get how they get there, but couldn't you just multiply by (x+1) and get a simple linear inequality?

help appreciated thanks )

1) What did you assume when you multiplied through by (x+1)?
2) You can, but dont have to, use a quadratic, but you have to be careful with point 1)

1) not too sure...? Whenever i've solved inequalities ive always just thought of it as a normal equation and then tackle the <0 or >0 at the end (i.e drawing a graph and putting the inequalities in last)

still struggling a bit with the logic behind the -1 tbh

For the logic behind the -1 part, you could recognize the problem is roughly
1/x < 1
This has solutions
x>1
x<0
Just sketch it.

What happens when you multiply an inequality by a negative number?

You have to flip the inequality and hence x>-1 im assuming?

Don't assume. Youve found one solution by when x+1>0. What happens when x+1<0? Work it through.

Ok, I've reworked the question a few times now and getting a hold of it thanks very much for the help!!