Let \( x \) represent the number of cars your friend details and \( y \) represent the number of SUVs he details. The earnings from detailing cars and SUVs can be expressed as follows:
- Earnings from cars: \( 55x \) (since he earns $55 per car)
- Earnings from SUVs: \( 70y \) (since he earns $70 per SUV)
Your friend wants to earn at least $750, so we can set up the inequality based on his total earnings:
\[ 55x + 70y \geq 750 \]
This is the linear inequality that can be used to determine how many cars \( x \) and SUVs \( y \) he must detail in order to earn at least $750.