The binary operation ⊕ ⊕ is defined by x ∗ ∗ y = xy - y - x for all real values x and y. If x ∗ ∗ 3 = 2∗ ∗ , find x

The binary operation $\oplus$ is defined by x $\ast$ y = xy - y - x for all real values x and y. If x $\ast$ 3 = 2$\ast$, find x

Answer Details

x $\ast$ y = xy - y - x, x $\ast$ 3 = 3x - 3 - x = 2x - 3
2 $\ast$ x = 2x - x - 2 = x - 2
∴ 2x - 3 = x - 2
x = -2 + 3
= 1