To solve this equation, we first need to simplify the left side by distributing the coefficients:

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

Next, we can combine the x terms and the constant terms:

1/3x - 3/8x - 1/3 - 3/8 = 1
(1/3 - 3/8)x - (1/3 + 3/8) = 1
(8/24 - 9/24)x - (8/24 + 9/24) = 1
(-1/24)x - (17/24) = 1
-1/24x - 17/24 = 1

Now, we can isolate the variable x by adding 17/24 to both sides and then multiplying by -24:

-1/24x = 1 + 17/24
-1/24x = 24/24 + 17/24
-1/24x = 41/24
x = (41/24) * -24
x = -41

Therefore, the solution to the equation is x = -41.