The base is 6.
In order to find this, we can set the legs equal to each other since legs have the same length in an isosceles triangle.
x + 1 = -x + 7
2x + 1 = 7
2x = 6
x = 3
Now that we have the value for x, we can plug into the equation to get the value for the base.
3x - 3 = base
3(3) - 3 = base
9 - 3 = base
6 = base