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Solve the inequality 9.5x−1.25<32 . 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. 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.
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.

1 answer

To solve the inequality \( 9.5x - 1.25 < 32 \), we start by isolating the variable \( x \).

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

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

    Performing this division: \[ \frac{33.25}{9.5} = 3.5 \]

Thus, we have the inequality: \[ x < 3.5 \]

Now, we need to express this solution on a number line. The solution \( x < 3.5 \) means that \( x \) can take any value less than 3.5, but not including 3.5 itself, since it is an open inequality.

We can denote this on a number line with an open point at 3.5, and an arrow extending leftward towards negative infinity.

Considering the options provided:

  • An open point is plotted on the number line between 3 and 4, which indicates that 3.5 is not included and a leftward arrow goes beyond negative 10.

This description matches one of the options given. Therefore, the correct choice is:

The option showing an open point between 3 and 4 with a leftward arrow.