To solve the inequality \( 10w + 213 \geq 299 \), we can follow these steps:
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Subtract 213 from both sides: \[ 10w \geq 299 - 213 \] \[ 10w \geq 86 \]
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Divide both sides by 10: \[ w \geq \frac{86}{10} \] \[ w \geq 8.6 \]
Since \( w \) represents the number of weeks, we typically round up to the nearest whole number because she can't wait for a fraction of a week. Thus, Ellie will need to wait at least 9 weeks to have enough money saved.
Among the provided options, the correct response is:
- \( w \geq 8.6 \)