The only thing I'm a little unclear on here is what you mean by
the "legs" of an isosceles triangle.
I'm going to assume that your isosceles triangle is standing on
the side you call the "base", and the "legs" are the two slanty ones,
standing up, which are the two equal sides.
With that set-up, x + 1 = -x + 7
Add x to each side: 2x + 1 = 7
Subtract 1 from each side: 2x = 6
Divide each side by 2 : x = 3
Finally, if the base is (3x - 3), then that's (3·3 - 3) = 6 .