To solve the inequality \( x + \frac{1}{3} > 4 \):
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First, subtract \(\frac{1}{3}\) from both sides: \[ x > 4 - \frac{1}{3} \] To perform the subtraction, convert 4 to a fraction: \[ 4 = \frac{12}{3} \quad \Rightarrow \quad x > \frac{12}{3} - \frac{1}{3} = \frac{11}{3} \]
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Now, convert \(\frac{11}{3}\) to a decimal or mixed number: \[ \frac{11}{3} = 3\frac{2}{3} \quad (\text{or } 3.6667) \]
Now, we need to express this on a number line. Since the inequality is \( x > \frac{11}{3} \) or \( x > 3\frac{2}{3} \), we need an open circle at \( 3\frac{2}{3} \) and a line extending to the right towards positive infinity.
Among the provided options, the correct graph would show:
- An open circle at \(3\frac{2}{3}\) (or the decimal equivalent \(3.67\))
- An arrow extending to the right, indicating all values greater than \(3\frac{2}{3}\).
The answer is: 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.
(Note: This description is correct since the actual circle marking should be at \(3\frac{2}{3}\). Please verify to ensure the exact nature as described above matches the correct location in the options given.)
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