Answer to Question #123755 in Abstract Algebra for Nii Laryea

Question

Consider the set X = R \ {-1} with the binary relation * defined by x * y = x + y + xy.
Find the solution for the equation 5 * x * 2 = -19.

Answer 1

We apply the operation once and receive: x * 2 = x+2+2x=3x+2. The second application yields

5 * (x * 2 )=5+3x+2+5(3x+2)=18x+17. One can check that it is associative. I.e.,

5 * (x * 2 ) = (5 * x ) * 2. The equation then reads 18x+17=-19. Solving the latter, we receive x=-2.

Answer: x=-2