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 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.

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 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 negative 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: \[ x > 4 - \frac{1}{3} \]

   To combine the numbers, convert \( 4 \) to a fraction: \[ 4 = \frac{12}{3} \]

   Thus, we get: \[ x > \frac{12}{3} - \frac{1}{3} = \frac{11}{3} \]

2. The solution \( x > \frac{11}{3} \) can also be expressed as \( x > 3 \frac{2}{3} \) or \( x > 3.67 \).

Now, we can visualize the solution on a number line:

• Since it’s an open inequality (greater than, not greater than or equal), we will use an open circle on \( \frac{11}{3} \) (approximately 3.67).
• The line will extend to the right (toward positive infinity).

From the options provided, the graph corresponding to the solution \( x > \frac{11}{3} \) (or \( x > 3.67 \)) would show an open circle at approximately 3.67 with an arrow extending to the right toward positive infinity.

So, the correct response would be:

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 five and two thirds. A line is drawn from the circle toward 10 with an arrow at the end.