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 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.
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Answer 1

To solve the inequality \(4x > 10\), we start by isolating \(x\):

1. Divide both sides by 4: \[ x > \frac{10}{4} \]
2. Simplifying \(\frac{10}{4}\) gives: \[ x > 2.5 \]

This means the solution to the inequality is all numbers greater than \(2.5\).

On a number line, this is represented by an open circle at \(2.5\) and a rightward arrow extending beyond \(10\).

From the options provided, the correct representation of the solution to the inequality \(4x > 10\) is:

• A number line with an open point plotted at \(2.5\) and a rightward arrow marked on the number line that originates at the open circle and goes beyond \(10\).

This corresponds to the option that states: "A number line ranges from negative 10 to 10 with an open point plotted at 2.5. A rightward arrow is marked on the number line that originates at the open circle and goes beyond 10."