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

Responses

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.

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.

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.

1 answer

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

  1. Subtract \( \frac{1}{3} \) from both sides:

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

  1. To perform the subtraction, convert 4 to a fraction:

\[ 4 = \frac{12}{3} \]

So,

\[ 4 - \frac{1}{3} = \frac{12}{3} - \frac{1}{3} = \frac{11}{3} \]

Thus the inequality simplifies to:

\[ x > \frac{11}{3} \]

Now, \(\frac{11}{3}\) is approximately \(3.67\) or \(3\frac{2}{3}\).

In the context of the given responses, look for a number line with an open circle marked above \(3\frac{2}{3}\) (which corresponds to \(\frac{11}{3}\)), and a line extending toward positive infinity (to the right).

From the descriptions you provided, the correct response would be the one that has an open circle above \(5\frac{2}{3}\) and a line extending toward negative 10—it seems like that would not match the solution \(x > \frac{11}{3}\).

The response that mentions an open circle marked at \(2\frac{1}{3}\) and extending toward negative infinity also does not match since the solution is greater than \(3\frac{2}{3}\).

The correct graph should include:

  • An open circle above \(3\frac{2}{3}\).
  • A line extending to the right toward positive infinity.

Therefore, if none of the provided descriptions match this criteria, it looks like the expected graph for \(x > \frac{11}{3}\) is not represented in the options given. Please double-check the descriptions of the images.