Solve for $x$: $x-2x+3x-4x+5x-6x+7x-8x+9x-10x=50$.
To solve for $x$, I need to simplify the left-hand side of the equation by combining the like terms that have $x$ as a factor. I can use the distributive property to factor out $x$ from each term and write the equation as: $x(1-2+3-4+5-6+7-8+9-10)=50$. Next, I can add and subtract the integers inside the parentheses and get: $x(-5)=50$. Now, to isolate $x$, I need to divide both sides of the equation by $-5$. This gives me: $x=\frac{50}{-5}=-10$. 