Question Solve for \( x \). Express your answer as a proper or improper fraction in simplest terms. \[ -\frac{1}{2}=-\frac{1}{6}+\frac{5}{11} x \]

To solve for \( x \), we start by isolating \( x \) in the equation: 1. First, add \( \frac{1}{6} \) to both sides: \[ -\frac{1}{2} + \frac{1}{6} = \frac{5}{11} x \] 2. We need a common denominator to combine the fractions on the left side. The least common multiple of 2 and 6 is 6. Rewriting \( -\frac{1}{2} \): \[ -\frac{3}{6} + \frac{1}{6} = \frac{5}{11} x \] 3. Now, combine the fractions: \[ -\frac{3}{6} + \frac{1}{6} = -\frac{2}{6} = -\frac{1}{3} \] So, we have: \[ -\frac{1}{3} = \frac{5}{11} x \] 4. To isolate \( x \), multiply both sides by the reciprocal of \( \frac{5}{11} \): \[ x = -\frac{1}{3} \cdot \frac{11}{5} = -\frac{11}{15} \] Thus, the solution is: \[ \boxed{-\frac{11}{15}} \] Here, we simplified the original equation step by step, effectively isolating \( x \) while ensuring all operations maintained the balance of the equation!