If $-2x - 7 = 7x + 2$, what is the value of $x$?
To solve for $x$, I want to isolate it on one side of the equation by using inverse operations. First, I can add $2x$ to both sides to get rid of the $-2x$ term on the left. This gives me $-7 = 9x + 2$. Next, I can subtract $2$ from both sides to get rid of the constant term on the right. This gives me $-9 = 9x$. Now, I can divide both sides by $9$ to get $x$ by itself. This gives me $x = -1$. I can check my answer by plugging it back into the original equation and seeing if it makes it true. If I do that, I get $-2(-1) - 7 = 7(-1) + 2$, which simplifies to $-5 = -5$, which is true. So $x = -1$ is the correct solution. 