We are given two equations to solve for $x$. The first equation is $3 - \frac{2x - 3}{3} = \frac{5 - x}{2}$. The second equation is $\frac{x + 3}{4} - \frac{x - 4}{2} = \frac{3}{8}$.

1. Problem Description

We are given two equations to solve for $x$.

The first equation is $3 - \frac{2x - 3}{3} = \frac{5 - x}{2}$.

The second equation is $\frac{x + 3}{4} - \frac{x - 4}{2} = \frac{3}{8}$.

2. Solution Steps

Let's solve the first equation: $3 - \frac{2x - 3}{3} = \frac{5 - x}{2}$.

Multiply both sides by 6 to eliminate fractions:

$6(3 - \frac{2x - 3}{3}) = 6(\frac{5 - x}{2})$

$18 - 2(2x - 3) = 3(5 - x)$

$18 - 4x + 6 = 15 - 3x$

$24 - 4x = 15 - 3x$

$24 - 15 = 4x - 3x$

$9 = x$

So $x = 9$.

Now, let's solve the second equation: $\frac{x + 3}{4} - \frac{x - 4}{2} = \frac{3}{8}$.

Multiply both sides by 8 to eliminate fractions:

$8(\frac{x + 3}{4} - \frac{x - 4}{2}) = 8(\frac{3}{8})$

$2(x + 3) - 4(x - 4) = 3$

$2x + 6 - 4x + 16 = 3$

$-2x + 22 = 3$

$-2x = 3 - 22$

$-2x = -19$

$x = \frac{-19}{-2}$

$x = \frac{19}{2}$

3. Final Answer

The solution to the first equation is $x = 9$.

The solution to the second equation is $x = \frac{19}{2}$.