Primarily use the Distributive Property to solve this equation.
3(5 - x) - 2(5 + x) = 3(x + 1)
Distribute the outer terms.
3(5) + 3(-x) - 2(5) - 2(x) = 3(x) + 3(1)
15 - 3x - 10 - 2x = 3x + 3
-3x - 2x + 15 - 10 = 3x + 3
-5x + 5 = 3x + 3
Now, isolate all x terms.
-5x + 5x + 5 = 3x + 5x + 3
5 = 8x + 3
5 - 3 = 8x + 3 - 3
2 = 8x
2/8 = 8x/8
x = 1/4