To solve the inequality \( \frac{2}{3}x \leq 5 \), we'll first isolate \( x \):
- Multiply both sides by \( \frac{3}{2} \) to eliminate the fraction (note that since \( \frac{3}{2} \) is positive, the direction of the inequality does not change):
\[ x \leq 5 \cdot \frac{3}{2} \]
- Calculate \( 5 \cdot \frac{3}{2} \):
\[ 5 \cdot \frac{3}{2} = \frac{15}{2} = 7.5 \]
So, the solution to the inequality is:
\[ x \leq 7.5 \]
On a number line, this solution would be represented by a closed point (indicating that 7.5 is included in the solution) at 7.5, with a leftward arrow extending towards negative infinity, since all values less than or equal to 7.5 are included in the solution.
From your options, the graph that correctly represents this solution is:
- A number line ranges from negative 10 to 10 with a closed point plotted at 7.5, with a leftward arrow that originates at the closed circle and goes beyond negative 10.
This graph visually shows that \( x \) can take any value less than or equal to 7.5.
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