Final answer:
To verify the equation x(y + z) = xy + yz, substitute the given values into both sides of the equation and simplify.
Step-by-step explanation:
To verify the equation x(y + z) = xy + yz for x = 1/2, y = 5/6, and z = -1/6, we substitute the given values into both sides of the equation.
On the left-hand side, we have 1/2(5/6 + (-1/6)) = 1/2(4/6) = 1/3.
On the right-hand side, we have (1/2)(5/6) + (5/6)(-1/6) = 5/12 - 5/36 = 15/36 - 5/36 = 10/36 = 1/3.
Since both sides of the equation simplify to 1/3, the given equation x(y + z) = xy + yz is verified.