The problem is to simplify the expression $\frac{3}{2} + \frac{4x-1}{3}$.

1. Problem Description

The problem is to simplify the expression $\frac{3}{2} + \frac{4x-1}{3}$.

2. Solution Steps

First, we need to find a common denominator for the two fractions. The least common multiple of 2 and 3 is

6. We rewrite each fraction with the common denominator 6:

$\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}$

$\frac{4x-1}{3} = \frac{(4x-1) \times 2}{3 \times 2} = \frac{8x-2}{6}$

Now we can add the two fractions:

$\frac{9}{6} + \frac{8x-2}{6} = \frac{9 + (8x - 2)}{6} = \frac{9 + 8x - 2}{6} = \frac{8x + 7}{6}$

3. Final Answer

$\frac{8x+7}{6}$