Solve the inequality 4x10 . Which of the following graphs shows the solution? (1 point) Responses 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. 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. 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. 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.

Question

Solve the inequality 4x>10 . Which of the following graphs shows the solution? (1 point) Responses 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. 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. 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. 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 need to isolate $ x $. 1. Divide both sides by 4: $$ x > \frac{10}{4} $$ Simplifying this gives: $$ x > 2.5 $$ This means the solution to the inequality is all values of $ x $ that are greater than $ 2.5 $. Now, let's analyze the given graph options: 1. **Option 1:** Open point at $ 2.5 $ with a rightward arrow (goes beyond 10) - This represents $ x > 2.5 $. 2. **Option 2:** Open point at $ 6 $ with a rightward arrow (goes beyond 10) - This represents $ x > 6 $. 3. **Option 3:** Open point at $ 2.5 $ with a leftward arrow (goes beyond negative 10) - This represents $ x < 2.5 $. 4. **Option 4:** Open point at $ 6 $ with a leftward arrow (goes beyond negative 10) - This represents $ x < 6 $. The correct solution graph for the inequality $ x > 2.5 $ is **Option 1**, which shows an open point at $ 2.5 $ with a rightward arrow indicating all values greater than $ 2.5 $.