a. \( 2 x+\frac{3}{5}=3+\frac{1}{6} \)

To solve the equation \( 2x + \frac{3}{5} = 3 + \frac{1}{6} \), first simplify the right side by finding a common denominator for the numbers involved. The common denominator for 1 and 6 is 6, so rewrite \(3\) as \( \frac{18}{6} \) to combine: \[ 3 + \frac{1}{6} = \frac{18}{6} + \frac{1}{6} = \frac{19}{6}. \] Now, your equation looks like this: \[ 2x + \frac{3}{5} = \frac{19}{6}. \] Next, subtract \( \frac{3}{5} \) from both sides. To do that, first convert \( \frac{3}{5} \) to have a common denominator with \( \frac{19}{6} \). The least common multiple of 5 and 6 is 30. So, \[ \frac{3}{5} = \frac{18}{30}, \quad \text{and} \quad \frac{19}{6} = \frac{95}{30}. \] Now your equation looks like: \[ 2x + \frac{18}{30} = \frac{95}{30}. \] Subtract \( \frac{18}{30} \) from both sides: \[ 2x = \frac{95}{30} - \frac{18}{30} = \frac{77}{30}. \] Finally, divide both sides by 2: \[ x = \frac{77}{60}. \] There's your solution: \( x = \frac{77}{60} \). Just to keep in mind, this result can be converted to a mixed number if needed: \( x = 1 \frac{17}{60} \), adding a fun twist to your answer!