\( \begin{array}{l}\text { Solve. (4 pts. each) } \\ \text { 16. } x-\frac{1}{6}=\frac{4}{5} \\ +\frac{1}{6}+\frac{1}{6}\end{array}=\frac{4}{5}+\frac{1}{6}=\frac{24}{30}+ \)

To solve the equation \( x - \frac{1}{6} = \frac{4}{5} + \frac{1}{6} + \frac{1}{6} \), we start by simplifying the right side. First, let's add the fractions on the right: 1. \( \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \) 2. Now substitute back into the equation: \[ x - \frac{1}{6} = \frac{4}{5} + \frac{1}{3} \] Next, we need a common denominator to add \( \frac{4}{5} \) and \( \frac{1}{3} \). The least common multiple of 5 and 3 is 15. Converting each fraction: - \( \frac{4}{5} = \frac{12}{15} \) - \( \frac{1}{3} = \frac{5}{15} \) Now add them: \[ \frac{12}{15} + \frac{5}{15} = \frac{17}{15} \] Now substituting back, we have: \[ x - \frac{1}{6} = \frac{17}{15} \] To isolate \( x \), add \( \frac{1}{6} \) to both sides: \[ x = \frac{17}{15} + \frac{1}{6} \] Again, we need a common denominator to add these. The least common multiple of 15 and 6 is 30. Convert each fraction: - \( \frac{17}{15} = \frac{34}{30} \) - \( \frac{1}{6} = \frac{5}{30} \) Now add them: \[ x = \frac{34}{30} + \frac{5}{30} = \frac{39}{30} \] Finally, simplify \( \frac{39}{30} \): \[ x = \frac{13}{10} \] So, the solution is \( x = \frac{13}{10} \) or \( 1.3 \).