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 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.
To solve the inequality 4x > 10, we need to isolate x on one side. We do this by dividing both sides of the inequality by 4:
4x > 10
x > 10/4
x > 2.5
This inequality means that x can be any number greater than 2.5. Now let's evaluate the provided number line options:
- A leftward arrow originating at the open circle at 6 and going beyond -10 does not represent the solution set since it implies x is less than 6, which is not correct.
- A rightward arrow originating at the open circle at 6 and going beyond 10 is also incorrect, as the solution set starts at 2.5, not 6.
- A leftward arrow originating at the open circle at 2.5 and going beyond -10 does not match our inequality either, as it implies x is less than 2.5, which contradicts x > 2.5.
None of the descriptions above match the correct representation of the inequality x > 2.5. The correct graph would include an open point plotted on the number line at 2.5 (to show that 2.5 is not included in the solution set) with a rightward arrow originating at that open circle and extending beyond 10 (to show that the solution set includes all numbers greater than 2.5).
Thus, none of the provided responses correctly represents the solution to the inequality 4x > 10.