Simplify -3/4r + 3 - 5/6r - 6

Question

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Answer 1

To simplify the expression \(-\frac{3}{4}r + 3 - \frac{5}{6}r - 6\), follow these steps:

1. Combine like terms: First, we'll group the \(r\) terms together and the constant terms together.

   \(-\frac{3}{4}r - \frac{5}{6}r + 3 - 6\)

2. Combine the constant terms:

   \(3 - 6 = -3\)

   So now the expression looks like:

   \(-\frac{3}{4}r - \frac{5}{6}r - 3\)

3. Combine the \(r\) terms: To do this, we need a common denominator for \(-\frac{3}{4}r\) and \(-\frac{5}{6}r\). The least common multiple of 4 and 6 is 12.

   • Convert \(-\frac{3}{4}r\) to a fraction with a denominator of 12:

   \(-\frac{3}{4} = -\frac{3 \times 3}{4 \times 3} = -\frac{9}{12}\)

   • Convert \(-\frac{5}{6}r\) to a fraction with a denominator of 12:

   \(-\frac{5}{6} = -\frac{5 \times 2}{6 \times 2} = -\frac{10}{12}\)

4. Now combine the \(r\) terms:

   \(-\frac{9}{12}r - \frac{10}{12}r = -\frac{9 + 10}{12}r = -\frac{19}{12}r\)

5. Put it all together:

   The complete simplified expression is:

   \(-\frac{19}{12}r - 3\)

So, the simplified form of the given expression is:

\[ -\frac{19}{12}r - 3 \]

Answer 2

are you POSITIVE this is correct?

Answer 3

Yes, I can confirm that the simplification I provided is correct. Here’s a step-by-step breakdown once more to assure you:

1. Start with the original expression: \[ -\frac{3}{4}r + 3 - \frac{5}{6}r - 6 \]

2. Combine like terms. Group the \(r\) terms and the constant terms: \[ -\frac{3}{4}r - \frac{5}{6}r + 3 - 6 \] Simplifying the constant terms: \[ 3 - 6 = -3 \] So, we have: \[ -\frac{3}{4}r - \frac{5}{6}r - 3 \]

3. Now, we need to combine the \(r\) terms \(-\frac{3}{4}r\) and \(-\frac{5}{6}r\).

   • Find a common denominator for 4 and 6, which is 12.
   • Convert \(-\frac{3}{4}r\): \[ -\frac{3}{4}r = -\frac{3 \times 3}{4 \times 3} = -\frac{9}{12}r \]
   • Convert \(-\frac{5}{6}r\): \[ -\frac{5}{6}r = -\frac{5 \times 2}{6 \times 2} = -\frac{10}{12}r \]

4. Now, combine the converted \(r\) terms: \[ -\frac{9}{12}r - \frac{10}{12}r = -\frac{19}{12}r \]

5. Put everything together: \[ -\frac{19}{12}r - 3 \]

So, in conclusion, the simplified expression is indeed: \[ -\frac{19}{12}r - 3 \]

If you have any further doubts or questions, feel free to ask!

Answer 4

hey bot

Answer 5

Hello! How can I assist you today?

Answer 6

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Answer 7

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