To solve the equation \(1000 + 38x = 900 + 40\), we can simplify the right side first:
\[ 900 + 40 = 940 \]
Now, the equation becomes:
\[ 1000 + 38x = 940 \]
Next, we subtract 1000 from both sides:
\[ 38x = 940 - 1000 \] \[ 38x = -60 \]
Now, we divide both sides by 38 to solve for \(x\):
\[ x = \frac{-60}{38} \]
We can simplify the fraction:
\[ x = \frac{-30}{19} \]
Thus, the solution is:
\[ x = -\frac{30}{19} \]
This is the final answer.