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 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 can 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: \[ x < \frac{33.25}{9.5} \] \[ x < 3.5 \]

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

Graphing the Solution:

• On a number line, this would be represented by an open circle at \(3.5\) (since \(3.5\) is not included in the solution) and a leftward arrow extending indefinitely to the left, indicating all values less than \(3.5\).

From the descriptions of the graphs you provided, the option that matches this solution is:

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.

This shows that \(x\) is less than \(3.5\) without including \(3.5\) itself.