Solve the inequality 4x10

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.

GPT-4o mini · Answer

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.