If $x^2- 2x = 0$ and $x \neq 0$, what is the value of $x$?
Dividing both sides by $x$ (noting that $x\ne0$), we have $x-2=0$ and so $x=\boxed{2}$.
2
Level 1
Algebra
Problem: If $x^2- 2x = 0$ and $x \neq 0$, what is the value of $x$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve the equation $x^2 - 2x = 0$, we can factor the left-hand side. The expression can be rewritten as $x(x - 2) = 0$. This factored form indicates that the product of two factors equals zero. According to the zero product property, at least one of the factors must be zero. Therefore, we set each factor equal to zero: 

1. $x = 0$
2. $x - 2 = 0$

From the second equation, we can solve for $x$ by adding $2$ to both sides, yielding $x = 2$. 

However, the problem states that $x \neq 0$. This condition eliminates the first solution, leaving us with the only valid solution. Thus, the value of $x$ that satisfies the original equation, while adhering to the given condition, is $2$.<|END_OF_LATENT|> The final answer is $2$.