To simplify the expression \( x + \frac{6}{3^2} - (2 \cdot 3) + 5 \), we can evaluate the expression step-by-step.
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Calculate \( 3^2 \): \[ 3^2 = 9 \]
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Substitute this back into the expression: \[ x + \frac{6}{9} - (2 \cdot 3) + 5 \]
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Simplify \( \frac{6}{9} \): \[ \frac{6}{9} = \frac{2}{3} \]
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Calculate \( 2 \cdot 3 \): \[ 2 \cdot 3 = 6 \]
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Substitute this back into the expression: \[ x + \frac{2}{3} - 6 + 5 \]
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Combine the constants \( -6 + 5 \): \[ -6 + 5 = -1 \]
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Substitute this back in: \[ x + \frac{2}{3} - 1 \]
Now the expression can be rewritten as: \[ x - 1 + \frac{2}{3} \]
To have a single fraction, we can express \(-1\) as \(-\frac{3}{3}\): \[ x - \frac{3}{3} + \frac{2}{3} = x - \frac{3 - 2}{3} = x - \frac{1}{3} \]
Thus, the final simplified expression is: \[ x - \frac{1}{3} \]
The simplified denominator involved in the original expression was \(9\) (from \(3^2\)) and in the fraction, it is \(3\) (from \(\frac{2}{3}\)).
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