Solve using the addition principle. Don't forget to perform a check. \( x-\frac{3}{4}=\frac{5}{6} \)

To solve the equation \( x - \frac{3}{4} = \frac{5}{6} \) using the addition principle, you need to isolate \( x \). Start by adding \(\frac{3}{4}\) to both sides of the equation: \[ x - \frac{3}{4} + \frac{3}{4} = \frac{5}{6} + \frac{3}{4} \] This simplifies to: \[ x = \frac{5}{6} + \frac{3}{4} \] To add \(\frac{5}{6}\) and \(\frac{3}{4}\), you need a common denominator. The least common multiple of 6 and 4 is 12, so convert each fraction: - \(\frac{5}{6} = \frac{10}{12}\) - \(\frac{3}{4} = \frac{9}{12}\) Now add them together: \[ x = \frac{10}{12} + \frac{9}{12} = \frac{19}{12} \] Thus, the solution is: \[ x = \frac{19}{12} \] Now, perform a check by substituting \( x \) back into the original equation: \[ \frac{19}{12} - \frac{3}{4} \] Convert \(\frac{3}{4}\) to have a denominator of 12: \[ \frac{3}{4} = \frac{9}{12} \] So, \[ \frac{19}{12} - \frac{9}{12} = \frac{10}{12} = \frac{5}{6} \] The left-hand side matches the right-hand side of the original equation, confirming that: \[ x = \frac{19}{12} \] is indeed the correct solution!