To simplify the expression \( \frac{1}{3} - 3\left(\frac{2}{7}x - 4\right) \), let's follow the steps carefully.
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Distribute the -3: \[ -3\left(\frac{2}{7}x - 4\right) = -3 \cdot \frac{2}{7}x + 3 \cdot 4 = -\frac{6}{7}x + 12 \]
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Combine it with \(\frac{1}{3}\): \[ \frac{1}{3} - \frac{6}{7}x + 12 \]
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Now, let's express everything under a common denominator. The least common denominator (LCD) of 3 and 1 would be 3, and we can rewrite 12 with a denominator of 3: \[ 12 = \frac{36}{3} \]
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Rewrite the expression with a common denominator: \[ \frac{1}{3} + \frac{36}{3} - \frac{6}{7}x \] \[ = \frac{1 + 36}{3} - \frac{6}{7}x = \frac{37}{3} - \frac{6}{7}x \]
So, the simplified form of the expression \( \frac{1}{3} - 3\left(\frac{2}{7}x - 4\right) \) is:
\[ \frac{37}{3} - \frac{6}{7}x \]
If you have other expressions to compare, please provide them, and I can help identify which ones are equivalent to this result.