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 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.

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 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.

Answer 1

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

\[ x > \frac{10}{4} \implies x > 2.5 \]

This means that the solution to the inequality is all values of \(x\) that are greater than 2.5.

Now, looking at the provided graph options:

1. The first graph shows an open point at 6 with a rightward arrow extending beyond 10. This implies \(x > 6\), which is too restrictive since \(x\) could start from 2.5.

2. The second graph shows an open point at 2.5 with a rightward arrow extending beyond 10. This correctly represents the solution \(x > 2.5\).

3. The third graph shows an open point at 2.5 with a leftward arrow going beyond negative 10. This implies \(x < 2.5\), which is not the correct solution.

4. The fourth graph shows an open point at 6 with a leftward arrow going beyond negative 10. This also does not represent the solution to the inequality.

Therefore, the correct graph is the second option, which accurately represents the solution \(x > 2.5\).