To simplify the expression \(-\frac{3}{4}r + 3 - \frac{5}{6}r - 6\), we can first combine like terms.
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Combine the constant terms:
The constant terms are \(3\) and \(-6\): \[ 3 - 6 = -3 \] -
Combine the terms with \(r\):
The \(r\) terms are \(-\frac{3}{4}r\) and \(-\frac{5}{6}r\). We need a common denominator to combine these fractions. The least common multiple of 4 and 6 is 12.Convert \(-\frac{3}{4}\) to a fraction with a denominator of 12: \[ -\frac{3}{4} = -\frac{3 \times 3}{4 \times 3} = -\frac{9}{12} \]
Convert \(-\frac{5}{6}\) to a fraction with a denominator of 12: \[ -\frac{5}{6} = -\frac{5 \times 2}{6 \times 2} = -\frac{10}{12} \]
Now combine these fractions: \[ -\frac{9}{12}r - \frac{10}{12}r = -\left(\frac{9 + 10}{12}\right)r = -\frac{19}{12}r \]
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Combine the results:
Now we have combined both parts: \[ -\frac{19}{12}r - 3 \]
Thus, the simplified expression is: \[ -\frac{19}{12}r - 3 \]