Simplify −3/4r + 3 − 5/6r − 6

Question

.(1 point)

Answer 1

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

1. Combine like terms:

   • Combine the \(r\) terms: \(-\frac{3}{4}r - \frac{5}{6}r\)
   • Combine the constant terms: \(3 - 6\)

2. Combining the constant terms: \[ 3 - 6 = -3 \]

3. Now we will combine the \(r\) terms: 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.

   Rewrite \(-\frac{3}{4}\) and \(-\frac{5}{6}\) with a denominator of 12: \[ -\frac{3}{4} = -\frac{3 \times 3}{4 \times 3} = -\frac{9}{12} \] \[ -\frac{5}{6} = -\frac{5 \times 2}{6 \times 2} = -\frac{10}{12} \]

   Now combine them: \[ -\frac{9}{12}r - \frac{10}{12}r = -\frac{19}{12}r \]

4. Now, putting everything together, we have: \[ -\frac{19}{12}r - 3 \]

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