To solve the inequality \(10w + 213 \geq 299\), we need to isolate \(w\).
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Subtract 213 from both sides:
\[ 10w \geq 299 - 213 \]
\[ 10w \geq 86 \]
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Now, divide by 10:
\[ w \geq \frac{86}{10} \]
\[ w \geq 8.6 \]
Since \(w\) represents the number of weeks, and it must be a whole number, we round up to the next whole number. Thus, Ellie needs at least 9 weeks to save enough money.
Therefore, the correct response is:
w ≥ 8.6 (which means she needs at least 9 weeks, since we consider whole weeks).