Ask a New Question
Menu

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 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 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.

1 answer

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

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

Simplifying \( \frac{10}{4} \) gives us \( \frac{5}{2} \) or \( 2.5 \). Thus, the solution to the inequality is:

\[ x > 2.5 \]

Now, on a number line, this means we would use an open circle (not including \( 2.5 \)) at \( 2.5 \) with a rightward arrow indicating all values greater than \( 2.5 \).

Based on your description of the graphs:

  • The correct representation is the one that shows an open point at \( 2.5 \) with a rightward arrow going beyond 10.

Thus, the correct graph is:

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.