You can subtract 4x from each side of the equation. Then you'll have the variable only on one side.
Before: 5x - 7 = 4x - 1
After: x - 7 = - 1
Now it's a lot easier to solve.
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I just noticed that you're giving 10 points for this one. That's a bunch, so I guess I owe you some more ... I really ought to go ahead and finish the solution:
Original equation: 5x - 7 = 4x - 1
Subtract 4x from each side: x - 7 = - 1
Add 7 to each side: x = 6
(Once you subtracted 4x from each side, there really wasn't much more left to do.)
