Solve the inequality 9.5x−1.25<32

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 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 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.

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 3 and 4. 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 \( 9.5x - 1.25 < 32 \), follow these steps:

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

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

This means the solution to the inequality is \( x < 3.5 \).

Now, let's analyze the possible graph options based on this solution:

• Since the inequality is strict ( < ), the endpoint \( x = 3.5 \) will be an open point on the number line.
• The solution extends to the left of 3.5, meaning it includes all numbers less than 3.5.

Among the options you provided:

• A number line with an open point plotted between 3 and 4 (after the 3) with a leftward arrow would properly represent \( x < 3.5 \).

Thus, the correct graph will be the one with an open point at \( x = 3.5 \) (just a little after 3) and a leftward arrow indicating all values less than 3.5.