Question

Solve the inequality 4x>10
. 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 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 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 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 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 begin by isolating \(x\).

1. Divide both sides of the inequality by 4:
\[
x > \frac{10}{4}
\]
\[
x > 2.5
\]

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

Now, we can evaluate the options based on this solution:

- **First Option:** Open point at 2.5 with a leftward arrow (incorrect, as this represents \(x < 2.5\)).
- **Second Option:** Open point at 2.5 with a rightward arrow (correct, as this represents \(x > 2.5\)).
- **Third Option:** Open point at 6 with a rightward arrow (incorrect, as this represents \(x > 6\), which is a more restricted solution).
- **Fourth Option:** Open point at 6 with a leftward arrow (incorrect, as this represents \(x < 6\)).

The correct graph is the **second option**: an open point at 2.5 with a rightward arrow extending beyond 10, indicating all numbers greater than 2.5.