To solve the inequality \( x + \frac{1}{3} > 4 \), we first isolate \( x \).
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Subtract \( \frac{1}{3} \) from both sides: \[ x > 4 - \frac{1}{3} \]
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To subtract \( \frac{1}{3} \) from \( 4 \), we can convert \( 4 \) to a fraction: \[ 4 = \frac{12}{3} \] Now, we have: \[ x > \frac{12}{3} - \frac{1}{3} = \frac{11}{3} \]
So, the solution to the inequality is: \[ x > \frac{11}{3} \]
On a number line, this would be represented by an open circle at \( \frac{11}{3} \) (approximately \( 3.67 \)) with a shaded line extending to the right, indicating all numbers greater than \( \frac{11}{3} \).
If you need to choose the correct graph representation, look for one that has:
- An open circle at \( \frac{11}{3} \)
- A shaded portion extending to the right from that point.