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 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 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 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.
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Answer 1

To solve the inequality \( 4x > 10 \), we need to isolate \( x \).

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

The solution \( x > 2.5 \) means that the graph should represent all values greater than 2.5 on the number line.

Looking at the options provided, the correct graph would be:

- A number line with an open point plotted at \( 2.5 \) and a rightward arrow indicating all values greater than \( 2.5 \).

So, the correct response is the one that shows an open point at \( 2.5 \) with a rightward arrow extending beyond \( 10 \). This corresponds to the list:
- "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."