7 - x + 2 = x - 3
7 + 2 + 3 = x + x
12 = 2x
x = 12 / 2
x = 6
sqrt(7 - x) + 2 = x - 3
sqrt(7 - x) = x - 3 - 2
sqrt(7- x) = x - 5
7 - x = (x - 5)^2
7 - x = x^2 - 10x + 25
x^2 - 10x + 25 + x - 7 = 0
x^2 - 9x + 18 = 0
(x - 3)(x - 6) = 0
x - 3 = 0 or x - 6 = 0
x = 3 or x = 6
Substituting x = 3 into the original equation, we have 4 = 0.
Thus, x = 3 is not a solution and we reject it.
Substituting x = 6 into the original equation, we have 3 = 3.
Hence, x = 6 is the only solution.