The minus sign belongs to the constant, and so is part of the constant when it is used to multiply the contents of the parentheses. The sign of a number defines the number as being positive or negative and it can’t be separated from the number. So in your example -2(x+1)=(-2×x)+(-2×1)=-2x-2.
-(2x-1) is the same as-1(2x-1). And the rule applies: (-1×2x)-(-1×1)=-2x+1. Minus acting on minus is plus.
To solve the inequality:
9-2x-2>5, 9-2>5+2x, 9-2-5>2x, 2>2x. Turn this round reversing the inequality by keeping the “point” pointing to 2x: 2x<2. Divide both sides by 2: x<1.