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The total cost for a single order of \( x \) cartridges can be calculated by considering both the cost of the ink cartridges and the flat shipping rate.
1. The cost for \( x \) cartridges is \( 19x \) (since each cartridge costs $19).
2. The shipping cost is a flat rate of $7.50.
Putting this together, the algebraic expression for the total cost \( C \) of an order of \( x \) cartridges is:
\[
C = 19x + 7.50
\]