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

Question

?(1 point)

Responses

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.

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.

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.

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.

Answer 1

To solve the inequality \( x + \frac{1}{3} > 4 \), we start by isolating \( x \):

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

2. Convert \( 4 \) to a fraction with a common denominator (3): \[ 4 = \frac{12}{3} \] So, \[ 4 - \frac{1}{3} = \frac{12}{3} - \frac{1}{3} = \frac{11}{3} \]

3. We now have: \[ x > \frac{11}{3} \] which is the same as: \[ x > 3 \frac{2}{3} \]

On a number line, this would be represented as an open circle at \( \frac{11}{3} \) (or \( 3 \frac{2}{3} \)) with a line extending to the right towards positive infinity.

Looking at the options given, the correct graph for the solution \( x > \frac{11}{3} \) is:

A number line with arrows at both ends, an open circle marked above \( 5 \frac{2}{3} \), and a line drawn from the circle toward \( 10 \) with an arrow at the end.

So, if you see an open circle at \( 5 \frac{2}{3} \) with a line extending towards the right (toward positive infinity), that is the correct representation of the solution \( x > \frac{11}{3} \).

None of the provided options correctly match the inequality \( x + \frac{1}{3} > 4 \), so it appears there may be a miscommunication or error in the problem set-up. Make sure to double-check the inequality or the corresponding graphs.