To solve the inequality \( \frac{5}{9}w \geq 8 \), we start by isolating \( w \).
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Multiply both sides of the inequality by \( 9 \) to eliminate the fraction: \[ 9 \cdot \left(\frac{5}{9}w\right) \geq 9 \cdot 8 \]
This simplifies to: \[ 5w \geq 72 \]
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Next, divide both sides by \( 5 \): \[ w \geq \frac{72}{5} \]
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Now, simplify \( \frac{72}{5} \): \[ \frac{72}{5} = 14.4 \]
Thus, the solution to the inequality is: \[ w \geq 14.4 \]
In interval notation, the solution can be expressed as: \[ [14.4, \infty) \]