To solve the inequality \( X + \frac{2}{3} < 9 \), follow these steps:
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Subtract \(\frac{2}{3}\) from both sides of the inequality:
\[ X < 9 - \frac{2}{3} \]
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To perform the subtraction, convert 9 into a fraction with a denominator of 3:
\[ 9 = \frac{27}{3} \]
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Now the equation becomes:
\[ X < \frac{27}{3} - \frac{2}{3} \]
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Subtract the fractions:
\[ X < \frac{27 - 2}{3} = \frac{25}{3} \]
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To convert \(\frac{25}{3}\) into a mixed number, divide 25 by 3:
\[ 25 \div 3 = 8 \quad \text{(the whole number part)} \] \[ 25 - (3 \times 8) = 25 - 24 = 1 \quad \text{(the remainder)} \]
Thus, \(\frac{25}{3} = 8 \frac{1}{3}\).
So the solution to the inequality \( X + \frac{2}{3} < 9 \) is:
\[ X < 8 \frac{1}{3} \]