If $|4x+2|=10$ and $x<0$, what is the value of $x$?
I know that the absolute value of an expression is always positive, regardless of the sign of the expression inside. So, $|4x+2|=10$ means that either $4x+2=10$ or $4x+2=-10$. However, the problem also says that $x<0$, which means that $x$ is negative. That rules out the possibility that $4x+2=10$, because if that were true, then $x=\frac{10-2}{4}=2$, which is not negative. So, I can focus on the equation $4x+2=-10$. To solve for $x$, I can subtract $2$ from both sides, and then divide by $4$. That gives me $x=\frac{-10-2}{4}=\frac{-12}{4}=-3$. So, the value of $x$ is $-3$.

