1. The problem asks to find the value of $x$ in the equation $$\frac{3x-1}{2} = 5.$$\n\n2. The formula used here is to solve linear equations by isolating the variable $x$.\n\n3. First, multiply both sides of the equation by 2 to eliminate the denominator:\n$$2 \times \frac{3x-1}{2} = 2 \times 5$$\nwhich simplifies to\n$$3x - 1 = 10.$$\n\n4. Next, add 1 to both sides to isolate the term with $x$:\n$$3x - 1 + 1 = 10 + 1$$\nwhich simplifies to\n$$3x = 11.$$\n\n5. Finally, divide both sides by 3 to solve for $x$:\n$$x = \frac{11}{3}.$$\n\n6. Therefore, the solution is $x = \frac{11}{3}$ or approximately 3.6667.