Solve the inequality 9.5x−1.25<32 witch gragh 1 2 3 or 4

Question

. Which of the following graphs shows the solution?(1 point)
Responses

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.
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.

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. 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.

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. 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. An open point is plotted on the number line between 3 and 4. A leftward arrow is marked on the number line that originates at the open point and goes beyond negative 10.

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.

Answer 1

To solve the inequality \( 9.5x - 1.25 < 32 \), we first isolate \( x \):

1. Add \( 1.25 \) to both sides: \[ 9.5x < 32 + 1.25 \] \[ 9.5x < 33.25 \]

2. Divide both sides by \( 9.5 \): \[ x < \frac{33.25}{9.5} \] \[ x < 3.5 \]

Now that we have the solution \( x < 3.5 \), we can determine how to graph it:

• The solution indicates that all values of \( x \) that are less than \( 3.5 \) are valid.
• Since \( 3.5 \) itself is not included, the graph should have an open point at \( 3.5 \) (not filled in) and an arrow extending leftward from this point.

Among the provided options, the correct graph should show:

• An open point at \( 3.5 \),
• A leftward arrow extending beyond the left side of the number line.

Based on the descriptions of the options provided, the second and third descriptions mention an open point plotted between \( 3 \) and \( 4 \), which is consistent with the solution we found.

The correct answer is likely the one that explicitly states that the open point is plotted just after \( 3 \) indicating that \( 3.5 \) is excluded from the solution.

Thus, the option showing an open point between \( 3 \) and \( 4 \) (just after \( 3 \)) with a leftward arrow extending beyond negative 10 would be the correct graph for the inequality \( 9.5x - 1.25 < 32 \).