Answer:
The first equation simplifies to 2X^2 - 9X = 0, while the second equation simplifies to X = -4
Explanation:
Let's examine each equation separately to determine if they are equivalent: 1) X•2•(X-4) = X To simplify this equation, we can distribute the 2 to the terms inside the parentheses: 2X(X-4) = X Now, let's multiply 2X by X and 2X by -4: 2X^2 - 8X = X Next, we'll move all the terms to one side of the equation: 2X^2 - 8X - X = 0 Simplifying further: 2X^2 - 9X = 0 Since this equation does not match the form of the second equation (X - 2X - 8 = X), they are not equivalent. 2) X - 2X - 8 = X To simplify this equation, let's combine like terms on the left side: -X - 8 = X Next, let's move all the terms to one side of the equation: -X - X = 8 Simplifying further: -2X = 8 Now, let's solve for X by dividing both sides of the equation by -2: X = 8 / -2 Simplifying: X = -4 Since this value of X satisfies the second equation (X - 2X - 8 = X), we can say that the second equation holds true for X = -4. To summarize, the equations X•2•(X-4) = X and X - 2X - 8 = X are not equivalent.