Solve the inequality 2/3x≤5

Question

. 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 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.
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.

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.

Answer 1

To solve the inequality $\frac{2}{3}x\le 5$, we can first isolate $x$.

1. Multiply both sides by the reciprocal of $\frac{2}{3}$, which is $\frac{3}{2}$: $$x\le 5\cdot \frac{3}{2}$$

2. Calculate $5\cdot \frac{3}{2}$: $$5\cdot \frac{3}{2}=\frac{15}{2}=7.5$$

So the solution to the inequality is: $$x\le 7.5$$

This means the solution set includes all values of $x$ that are less than or equal to $7.5$.

Now, looking at the graph options you provided, you need to find the one that shows a closed point at $7.5$ with a leftward arrow, indicating all numbers to the left of $7.5$.

The correct graph should have:

• A closed point at $7.5$
• A leftward arrow extending towards negative infinity.

Based on your description, the fourth option is the correct one: "A number line ranges from negative 10 to 10 with a closed point plotted at 7.5 and a leftward arrow originating at the closed circle and going beyond negative 10."

Therefore, the answer is the fourth graph.