10. \( \frac{3}{4}-\frac{2}{3} x=\frac{11}{12} \)

To solve the equation \( \frac{3}{4} - \frac{2}{3} x = \frac{11}{12} \), we first need to isolate the term with \( x \). Let's get everything on one side by subtracting \( \frac{3}{4} \) from both sides: \[ -\frac{2}{3} x = \frac{11}{12} - \frac{3}{4} \] Next, we need a common denominator to combine the fractions on the right. The least common multiple of 12 and 4 is 12: \[ \frac{3}{4} = \frac{9}{12} \] So, substituting this back in, we have: \[ -\frac{2}{3} x = \frac{11}{12} - \frac{9}{12} = \frac{2}{12} \] Now simplifying \( \frac{2}{12} \) gives us \( \frac{1}{6} \): \[ -\frac{2}{3} x = \frac{1}{6} \] To eliminate the negative, we can multiply both sides by -1: \[ \frac{2}{3} x = -\frac{1}{6} \] Next, to isolate \( x \), we can multiply both sides by the reciprocal of \( \frac{2}{3} \): \[ x = -\frac{1}{6} \cdot \frac{3}{2} = -\frac{3}{12} = -\frac{1}{4} \] So, the solution to the equation is: \[ x = -\frac{1}{4} \]