correct answer is: a) 5\frac{1}{3}

Explanation

\frac{3x\ -\ 1}{5}\ -\ \frac{1\ +\ x}{2}\ =\ 3\ -\ \frac{x\ -\ 1}{2}
\rightarrow\ \frac{2\left(3x\ -\ 1\right)\ -\ 5\left(1+x\right)}{10}\ =\ \frac{\left(2\times3\right)\ -\ 1\left(x\ -1\right)}{2}
\rightarrow\ \frac{6x\ -\ 2\ -\ 5\ -\ 5x}{10}\ =\ \frac{6\ -\ x\ -1}{2}
\rightarrow\ \frac{x\ -\ 7}{10}\ =\ \frac{5\ -\ x}{2}
\rightarrow\ 10\left(5\ -\ x\right)\ =\ 2\left(x\ -7\right) _{[cross multiply]}
\rightarrow\ 50\ -\ 10x\ =\ 2x\ – 14
\rightarrow\ -10x\ -\ 2x\ =\ -14\ -50 _{[interchange]}
\rightarrow\ -12x\ =\ -64
\rightarrow\ x\ =\ \frac{-64}{-12}
\rightarrow\ x\ =\ \frac{16}{3} or 5\frac{1}{3}
Ans: 5\frac{1}{3}

Another way to ask this same question is:
1. How to solve the equation (3x – 1) / (5 – 1) + x / 2 = (3 – x – 1) / 2?
2. Step-by-step solution for the equation (3x – 1) / (5 – 1) + x / 2 = (3 – x – 1) / 2.
3. What are the steps to simplify and solve (3x – 1) / (5 – 1) + x / 2 = (3 – x – 1) / 2?
4. Solve the algebraic equation (3x – 1) / (5 – 1) + x / 2 = (3 – x – 1) / 2 with explanations.
5. Explanation and solution for the equation involving fractions: (3x – 1) / (5 – 1) + x / 2 = (3 – x – 1) / 2.