Solve the inequality 9.5x−1.25<32 . Which of the following graphs shows the solution?(1 point) Responses Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line between 3 and 4, just after the 3. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10. Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 4 and 5, just before 5. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10. Image with alt text: A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.
To solve the inequality 9.5x - 1.25 < 32, we can start by isolating the variable x.
Adding 1.25 to both sides, we get:
9.5x < 32 + 1.25
9.5x < 33.25
Dividing both sides by 9.5, we get:
x < 33.25/9.5
x < 3.5
So the solution to the inequality is x < 3.5.
Now let's look at the given graphs:
- Image 1: The open point is plotted between 3 and 4 on the number line, just after 3. The leftward arrow goes beyond -10. This graph does not represent the solution x < 3.5.
- Image 2: The closed point is plotted between 4 and 5 on the number line, just before 5. The leftward arrow goes beyond -10. This graph also does not represent the solution x < 3.5.
- Image 3: The closed point is plotted between 3 and 4 on the number line. The leftward arrow goes beyond -10. This graph represents the solution x < 3.5.
Therefore, the correct graph that shows the solution to the inequality is Image 3.