On the set (A=\mathbb{R}\setminus{-1}), the operation (a*b=a+b+ab) is defined. If (x) is the inverse of (5), what is the value of (x*2)?

Correct answer: (-\frac{1}{2})

Step 1: The identity element is (0) because (a*0=a). Step 2: (5*x=0\Rightarrow 5+x+5x=0\Rightarrow 6x=-5\Rightarrow x=-\frac{5}{6}). Step 3: Now (x*2=-\frac{5}{6}+2-\frac{10}{6}=-\frac{1}{2}). In exams, after finding the inverse, substitute it carefully into the next operation.