Explanation:
You start with x+1=7x-5
Basically you want all the x's on one side and all the constants on the other
(x+1)+5=(7x-5)+5, to get rid of the 5 on the right side
(x+6)-x=7x-x, to get rid of the x on the left side
We are now left with 6x=6
No we simplify, 6x/6=6/6
Now we have x=1, which is the answer
I hope this made sense.