Which of the following shows the graph of the solution to x+1 2/3>4

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 on the tick line above two and one third. A line 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 on the tick line above two and one third. 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 on the tick line above 5 and two thirds. 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 on the tick line above 5 and two thirds. 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 on the tick line above two and one third. 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 on the tick line above two and one third. A line is drawn from the circle 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 on the tick line above 5 and two thirds. A line 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 on the tick line above 5 and two thirds. A line is drawn from the circle toward negative 10 with an arrow at the end.

Answer 1

To solve the inequality \( x + \frac{1}{3} > 4 \), we first need to isolate \( x \):

1. Subtract \( \frac{1}{3} \) from both sides: \[ x > 4 - \frac{1}{3} \]

2. Convert 4 to a fraction with a denominator of 3: \[ 4 = \frac{12}{3} \]

3. Now, perform the subtraction: \[ 4 - \frac{1}{3} = \frac{12}{3} - \frac{1}{3} = \frac{11}{3} \]

Thus, the inequality simplifies to: \[ x > \frac{11}{3} \]

Now, \( \frac{11}{3} \) is equal to \( 3 \frac{2}{3} \). On a number line, you would represent this by placing an open circle at \( \frac{11}{3} \) (or \( 3 \frac{2}{3} \)), and shading to the right to indicate all values greater than \( \frac{11}{3} \).

Looking at the options:

1. Option 1 shows an open circle at \( 2 \frac{1}{3} \) and arrows toward negative values (incorrect).
2. Option 2 shows an open circle at \( 5 \frac{2}{3} \) and arrows toward positive values (not correct).
3. Option 3 shows an open circle at \( 2 \frac{1}{3} \) and arrows toward positive values (incorrect).
4. Option 4 shows an open circle at \( 5 \frac{2}{3} \) and arrows toward negative values (incorrect).

None of the options provided exactly match the correct placement at \( 3 \frac{2}{3} \) with shading toward the right, but from the choices given, Option 3 comes closest to indicating a direction toward the positive side (shading right) although marked at the wrong position.

For the correct solution of \( x > \frac{11}{3} \), the answer would involve an open circle at \( \frac{11}{3} \) with shading towards the right.

In this case, the best choice among those given would be Option 3, even though it is not perfectly correct due to the position of the open circle.