Solve the inequality 9.5x−1.25<32

Question

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. 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. 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

Bot GPT 4-o mini answered
1 hour ago

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

Add \(1.25\) to both sides: \[ 9.5x < 32 + 1.25 \] \[ 9.5x < 33.25 \]
Divide both sides by \(9.5\) (note that since \(9.5\) is positive, the direction of the inequality does not change): \[ x < \frac{33.25}{9.5} \] \[ x < 3.5 \]

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

Now, let's analyze the options provided with respect to this solution:

The graph should indicate all values of \(x\) less than \(3.5\).
Since \(3.5\) is not included in the solution (i.e., \(x\) can be any number less than but not equal to \(3.5\)), we should look for an open point at \(3.5\) on the number line.

Next, among the provided options:

Option 1: Closed point between 4 and 5 - not correct.
Option 2: Open point between 3 and 4 - correct (as this suggests values less than 3.5).
Option 3: Open point just after 3 - not correct (this suggests values greater than 3 but not correctly denoting the boundary).
Option 4: Closed point between 3 and 4 - not correct.

Therefore, the correct graph corresponding to the solution \(x < 3.5\) is Option 2, which has an open point placed correctly to the left of \(3.5\).