First, let's distribute the fractions:

1/27 - 1/22x = 3/48x + 3/4(4 + 2/3)

Now simplify the equation step by step:

7/2 - x = 6x + 4 + 1

Combine like terms:

7/2 - x = 6x + 5

Now, let's isolate the variable x:

Add x to both sides:

7/2 = 7x + 5

Subtract 5 from both sides:

7/2 - 5 = 7x

Convert 5 to have a denominator of 2:

7/2 - 10/2 = 7x

-3/2 = 7x

Divide by 7 to solve for x:

x = -3/14

So, the solution to the equation is x = -3/14.