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. 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.
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. 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, B, C, or D?

Answer 1

To solve the inequality \(9.5x - 1.25 < 32\), follow these steps:

1. First, add \(1.25\) to both sides of the inequality: \[ 9.5x < 32 + 1.25 \] \[ 9.5x < 33.25 \]

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

Now, the solution to the inequality is \(x < 3.5\), which means that all numbers less than \(3.5\) satisfy the inequality.

In terms of graphing this solution on a number line:

• You would place an open point at \(3.5\) (indicating that \(3.5\) itself is not included in the solution).
• You would draw an arrow to the left from \(3.5\), indicating that all values less than \(3.5\) are part of the solution.

Based on the description, the correct representation of this solution would have an open point at \(3.5\) and an arrow extending leftwards.

Since there are multiple options presented, we can choose from:

• A number line with an open point just after \(3\) (indicating it being near \(3.5\)) and a left arrow suggests that it is the region for \(x < 3.5\).

Looking at the responses, the one that confirms the described condition of \(x < 3.5\) is:

Option A: A number line is shown with an open point just after \(3\) between \(3\) and \(4\) and a leftward arrow extending indefinitely.

So, the answer is A.