Solve the inequality 4x>10

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. An open point is plotted on the number line at 6. A leftward arrow is marked on the number line that originates at the open 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. An open point is plotted on the number line at 6. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 2.5. A rightward arrow is marked on the number line that originates at the open circle and goes beyond 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 2.5. A rightward arrow is marked on the number line that originates at the open circle and goes beyond 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 2.5. A leftward arrow is marked on the number line that originates at the open 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. An open point is plotted on the number line at 2.5. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 6. A rightward arrow is marked on the number line that originates at the open circle and goes beyond 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 6. A rightward arrow is marked on the number line that originates at the open circle and goes beyond 10.

Answer 1

To solve the inequality \(4x > 10\), we first divide both sides by 4:

\[ x > \frac{10}{4} \]

\[ x > 2.5 \]

This means that the solution set includes all values of \(x\) that are greater than 2.5.

Now, let's analyze the possible answer choices based on our solution:

1. Open point at 6 with a leftward arrow: This would indicate that values less than 6 are included, which does not match our solution.

2. Open point at 2.5 with a rightward arrow: This correctly indicates that values greater than 2.5 are included.

3. Open point at 2.5 with a leftward arrow: This would imply values less than 2.5, which is incorrect.

4. Open point at 6 with a rightward arrow: This suggests values greater than 6, which is incorrect because we need values greater than 2.5.

The correct option is the second response: a number line with an open point at 2.5 and a rightward arrow, indicating that \(x\) can take any value greater than 2.5.