To solve the inequality \( x < 206 \cdot 504 - 208 \cdot 401 \), we first need to calculate the right-hand side.
Calculate \( 206 \cdot 504 \): \[ 206 \cdot 504 = 103224 \]
Calculate \( 208 \cdot 401 \): \[ 208 \cdot 401 = 83408 \]
Now, subtract the second product from the first: \[ 103224 - 83408 = 19816 \]
So we have: \[ x < 19816 \]
The solution to the inequality is \( x < 19816 \).