To solve this equation, we first need to simplify the left side of the equation:

1 1/12 + 3.75 = 13/12 + 3.75 = 13/12 + 45/12 = 58/12 = 4.83

Now we can rewrite the equation with the simplified left side:

4.83 - (-x) = 4.5

Next, we can simplify the equation further by getting rid of the negative sign in front of the x:

4.83 + x = 4.5

Now, we need to isolate x by subtracting 4.83 from both sides of the equation:

x = 4.5 - 4.83
x = -0.33

Therefore, the solution to the equation is x = -0.33.