To solve the inequality \(8x - 7 \geq 97\) for \(x\) (the number of plates), we can follow these steps:
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Start with the original inequality: \[ 8x - 7 \geq 97 \]
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Add 7 to both sides: \[ 8x \geq 104 \]
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Now, divide both sides by 8: \[ x \geq \frac{104}{8} \] \[ x \geq 13 \]
Thus, India would have to sell at least 13 plates to reach her goal of $97 after accounting for the cost of the drinks.