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Solve the inequality 2/3x≤5

. Which of the following graphs shows the solution? (1 point)
Responses

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 7.5. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 7.5. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 5 start fraction 2 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 5 start fraction 2 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 4 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 4 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 3 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

1 answer

To solve the inequality \( \frac{2}{3}x \leq 5 \), we first isolate \( x \).

  1. Multiply both sides by \( \frac{3}{2} \) to eliminate the fraction: \[ x \leq 5 \cdot \frac{3}{2} \]

  2. Perform the multiplication: \[ x \leq \frac{15}{2} = 7.5 \]

The solution to the inequality is \( x \leq 7.5 \).

On a number line, this is represented by a closed point at \( 7.5 \) with a leftward arrow indicating all values to the left of \( 7.5 \).

Looking through the provided options, the graph that accurately represents this solution is:

  • A number line with a closed point at \( 7.5 \) and a leftward arrow extending beyond negative \( 10 \).

This corresponds to the first option you mentioned in your question.