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

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

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

  2. Convert 4 into a fraction: \[ 4 = \frac{12}{3} \] Therefore, \[ x > \frac{12}{3} - \frac{1}{3} = \frac{11}{3} \]

Now convert \(\frac{11}{3}\) to a mixed number: \[ \frac{11}{3} = 3 \frac{2}{3} \]

In decimal form, \(\frac{11}{3} \approx 3.67\) or \(3.666...\).

The solution to the inequality is \( x > \frac{11}{3} \) or \( x > 3 \frac{2}{3} \).

Graph Representation:

On a number line:

  • You would have an open circle at \( \frac{11}{3} \) (which is the same as \(3 \frac{2}{3}\)).
  • The line should extend to the right toward positive infinity, indicating all numbers greater than \( \frac{11}{3} \).

Correct Option:

From the provided responses, the correct option 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 \( 3 \frac{2}{3} \). A line is drawn from the circle toward 10 with an arrow at the end.