To simplify the expression \(-\frac{3}{4}r + 3 - -\frac{5}{6}r - 6\), follow these steps:
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Eliminate the negative sign in front of -5/6r: \(-\frac{3}{4}r + 3 + \frac{5}{6}r - 6\)
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Combine like terms:
- For the constant terms: \(3 - 6 = -3\)
- For the variable terms: Combine \(-\frac{3}{4}r\) and \(\frac{5}{6}r\).
To combine \(-\frac{3}{4}r\) and \(\frac{5}{6}r\), we need a common denominator. The least common multiple of 4 and 6 is 12.
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Convert \(-\frac{3}{4}r\) to twelfths: \[ -\frac{3}{4}r = -\frac{3 \times 3}{4 \times 3}r = -\frac{9}{12}r \]
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Convert \(\frac{5}{6}r\) to twelfths: \[ \frac{5}{6}r = \frac{5 \times 2}{6 \times 2}r = \frac{10}{12}r \]
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Now combine the variable terms: \(-\frac{9}{12}r + \frac{10}{12}r = \frac{10 - 9}{12}r = \frac{1}{12}r\)
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Putting it all together: \[ \frac{1}{12}r - 3 \]
Therefore, the simplified expression is: \[ \frac{1}{12}r - 3 \]
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