To evaluate the expression \( x + \frac{6}{3^2} - (2 \times 3) + 5 \), we first handle the operations in sequence, following the order of operations (PEMDAS/BODMAS).
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Calculate \( 3^2 \): \[ 3^2 = 9 \]
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Substitute \( 9 \) into the expression: \[ x + \frac{6}{9} - (2 \times 3) + 5 \]
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Simplify \( \frac{6}{9} \): \[ \frac{6}{9} = \frac{2}{3} \]
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Calculate \( 2 \times 3 \): \[ 2 \times 3 = 6 \]
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Substitute these values: \[ x + \frac{2}{3} - 6 + 5 \]
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Simplifying further: \[ -6 + 5 = -1 \] Therefore, the expression simplifies to: \[ x + \frac{2}{3} - 1 \]
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Finally, rewrite \(-1\) as \(-\frac{3}{3}\) to combine terms: \[ x + \frac{2}{3} - \frac{3}{3} = x - \frac{1}{3} \]
Since the prompt asks for the simplified denominator of the initial expression (regardless of \( x \)), we only need the fraction \(\frac{6}{9}\) to determine that. The simplified denominator during this step is \(3\), but we must consider if the expression was misstated regarding the options given, as the phrase “the simplified denominator” may pertain to the final expression form.
Thus, the final interpretation leads us towards the choices:
- None of the available choices (8, 56, 26, -2) directly reflect the completed denominator we explored.
To check connections to the answers: If you interpret \(3^2\) (which affects denominators in results), you might isolate responses toward a curative constant: If simplified further, the main fraction could hold evaluative positions among some constants not shown.
But interpreting this properly infers considering basic forms, leading back to basic fraction results without constant dependency yielding currently unstated answers. So there could be a revision on phrasing or relation between how "denominator" in the explicit articulated form positions specifically through fractions involved.
Final assessments remain then completed fractions will yield \(x - 1/3\) retained, rendering evaluative consistency around expressed options misconnected through processed states in early-stage fraction forms noted versus foundational states.
Thus there remains a structural clarity about inventing or shifting toward convincing framing akin to residually unspecified options through complex layouts in representation denomination computations; needing clearer paths resolves this misconception around defining outputs rather than factional determinants within such, keeping track through legible staged arithmetic informs whether specifics detail variations through constructed forms adequately noted before concluding beyond \(x - 1/3\) actions as is structured.
Under clearer renditions, we could clarify denoting paths \(3\) remains while options misaligned, leading confusion.