To solve the inequality \( \frac{2}{3}x \leq 5 \), we first isolate \( x \).
- Multiply both sides of the inequality by \( \frac{3}{2} \) to get rid of the fraction:
\[ x \leq 5 \cdot \frac{3}{2} \]
- Calculate \( 5 \cdot \frac{3}{2} \):
\[ 5 \cdot \frac{3}{2} = \frac{15}{2} = 7.5 \]
So we have:
\[ x \leq 7.5 \]
This means the solution set includes all values of \( x \) that are less than or equal to \( 7.5 \).
On a number line, this would be represented by a closed circle at \( 7.5 \) (indicating that \( 7.5 \) is included) and a leftward arrow indicating all values to the left of \( 7.5 \).
Among the response options given, the correct graph is:
- A number line with a closed point plotted on the number line at \( 7.5 \), and a leftward arrow marked on the number line that originates at the closed circle and goes beyond negative 10.
This represents the solution \( x \leq 7.5 \) accurately.
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