Question

Simplify −3/4r + 3 − 5/6r − 6
.(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:
\[
-\frac{19}{12}r - 3
\]