Question

Simplify \(-\frac{3}{4}r\ +\ 3\ -\ \frac{5}{6}r\ -\ 6\). (1 point)

Answer 1

To simplify the expression \(-\frac{3}{4}r + 3 - \frac{5}{6}r - 6\), we will first combine like terms.

1. Combine the constant terms: \(3 - 6\).
\[
3 - 6 = -3
\]

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

To combine the \(r\) terms, we need a common denominator. The least common multiple of \(4\) and \(6\) is \(12\).
- Convert \(-\frac{3}{4}r\) to have a denominator of \(12\):
\[
-\frac{3}{4}r = -\frac{3 \times 3}{4 \times 3}r = -\frac{9}{12}r
\]
- Convert \(-\frac{5}{6}r\) to have a denominator of \(12\):
\[
-\frac{5}{6}r = -\frac{5 \times 2}{6 \times 2}r = -\frac{10}{12}r
\]

3. Now, combine these two converted terms:
\[
-\frac{9}{12}r - \frac{10}{12}r = -\frac{9 + 10}{12}r = -\frac{19}{12}r
\]

4. Putting it all together, the simplified expression is:
\[
-\frac{19}{12}r - 3
\]

Thus, the simplified expression is \(\boxed{-\frac{19}{12}r - 3}\).