First, you must subtract 5x from both sides, so it would look like this:
3x-7=5x+1
-5x -5x
This would leave you with -2x-7=1. Now it's a normal 2-step equation. Add 7 to both sides, like this:
-2x-7=1
+7 +7
So, now it is -2x=8. Now you divide by -2 by both sides.
-2x=8
-2 -2
Your answer would be -4.
So, x=-4