Let's first distribute the 1/4 on the right side of the equation:

1/4(4 + x) = 3/8x + 1

1/4 4 = 1
1/4 x = 1/4x

So, the equation becomes:

1 + 1/4x = 3/8x + 1

Now, let's simplify the equation:

1/4x = 3/8x

Now, we can solve for x.

Multiplying through by 8 to eliminate the fractions, we get:

2x = 3x

Subtract x from both sides:

2x - x = 3x - x

x = 0

So, the solution for x is 0.