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To find the total cost for an order of \( x \) ink cartridges, we can break down the costs as follows:
1. Each ink cartridge costs $19.
2. There is a flat shipping fee of $7.50, regardless of the number of cartridges ordered.
For \( x \) cartridges, the cost for the cartridges is \( 19x \), and the shipping cost is \( 7.50 \).
Therefore, the algebraic expression for the total cost \( C \) as a function of the number of cartridges \( x \) is:
\[
C = 19x + 7.50
\]