Which of the following shows the graph of the solution to x−0.3<3.2

Question

?(1 point)
Responses

1.A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked at 2.9. A ine is drawn from the circle toward negative 10 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked at 2.9. A line is drawn from the circle toward negative 10 with an arrow at the end.

2.A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked at 3.5. A line is drawn from the circle toward 10 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked at 3.5. A line is drawn from the circle toward 10 with an arrow at the end.

3.A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked at 2.9. A line is drawn from 2.9 toward 10 with an arrow at the end.
Image with alt text: A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked at 2.9. A line is drawn from 2.9 toward 10 with an arrow at the end.

4.A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked at 3.5. A line is drawn from the circle toward negative 10 with an arrow at the end.

Answer 1

To solve the inequality \(x - 0.3 < 3.2\), we need to isolate \(x\):

1. Start with the inequality: \[ x - 0.3 < 3.2 \]

2. Add \(0.3\) to both sides: \[ x < 3.2 + 0.3 \] \[ x < 3.5 \]

The solution to the inequality is \(x < 3.5\), which means the graph should show a number line with an open circle at \(3.5\) and a line extending to the left (towards negative infinity).

Looking at the options:

1. Option 1: Open circle at 2.9, line extending left → This is incorrect (should be at 3.5).
2. Option 2: Open circle at 3.5, line extending right → This is incorrect (should be extending left).
3. Option 3: Open circle at 2.9, line extending right → This is incorrect (should be at 3.5).
4. Option 4: Open circle at 3.5, line extending left → This is correct.

Therefore, the correct response is Option 4: A number line with an open circle at 3.5 and a line drawn from the circle toward negative infinity.