If |2x - 5| = 11 and x is negative, what is the value of x?

An absolute value equation splits into two cases. Case 1: $2x - 5 = 11$ gives $2x = 16$, so $x = 8$. Case 2: $2x - 5 = -11$ gives $2x = -6$, so $x = -3$. The problem states that $x$ is negative, so we keep only $x = -3$. Check: $|2(-3) - 5| = |-11| = 11$. Common wrong answers: 8 is the other valid solution to the equation but it is positive, so it is excluded. Another wrong answer is $-8$, which results from solving the second case incorrectly, and a third is 3, from dropping the sign.