To solve the inequality \( \frac{2}{3}x \leq 5 \), follow these steps:
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Isolate \( x \): Multiply both sides of the inequality by \( \frac{3}{2} \) to eliminate the fraction. Keep in mind that we do not need to flip the inequality sign since we're multiplying by a positive number.
\[ x \leq 5 \cdot \frac{3}{2} \]
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Calculate the right side: \[ 5 \cdot \frac{3}{2} = \frac{15}{2} = 7.5 \]
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Conclusion: The solution to the inequality is: \[ x \leq 7.5 \]
The graph representing the solution will have a closed circle (or dot) at \( x = 7.5 \) and will shade all values to the left of that point (indicating that \( x \) can take any value less than or equal to 7.5).
If you describe the options for the graphs, I can help you identify which one corresponds to this solution!
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