Solve the inequality 4x>10 . Which of the following graphs shows the solution? (1 point)

Question

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 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 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.

Answer 1

To solve the inequality \(4x > 10\), we need to isolate the variable x by dividing both sides of the inequality by 4:

\(4x > 10\)

Divide both sides by 4:

\(x > \frac{10}{4}\)

\(x > 2.5\)

This means x can take any value greater than 2.5. Now, we look at the descriptions provided for the number line representations to determine which graph correctly represents the solution to the inequality.

We are looking for a number line that shows all values greater than 2.5, which will be represented by an open circle at 2.5 and a rightward arrow indicating all numbers to the right of 2.5.

Based on the descriptions you provided:

- The first description represents all values less than 6, which is not the correct solution.

- The second description represents all values greater than 6, which is not the correct solution.

- The third description represents all values less than 2.5, which is not the correct solution.

- The fourth description matches the solution perfectly: a number line with an open point at 2.5 and a rightward arrow representing all values greater than 2.5.

Therefore, the correct graph is the one described by the fourth option:

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.