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Solve the inequality 2/3 x ≤ 5

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

1.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.

2.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.
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 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.

3.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.

4.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.

1 answer

To solve the inequality \( \frac{2}{3} x \leq 5 \), we first isolate \( x \) by multiplying both sides by \( \frac{3}{2} \):

\[ x \leq 5 \times \frac{3}{2} \] \[ x \leq \frac{15}{2} \] \[ x \leq 7.5 \]

This means the solution is all values of \( x \) that are less than or equal to \( 7.5 \).

Now we look for the correct graph representation:

  • The graph should have a closed point (inclusive) at \( 7.5 \) and should extend to the left towards negative infinity.

Among the responses you provided, we can identify the correct one:

  1. Graph 1 shows a closed point at \( \frac{2}{3} \) which does not match.
  2. Graph 2 has a closed point at \( 3 \frac{1}{3} \) which does not match.
  3. Graph 3 has a closed point at \( 4 \frac{1}{3} \) which does not match.
  4. Graph 4 shows a closed point at \( 7.5 \) which matches our solution, extending left.

Therefore, the correct response is 4.