Question

Algebraic Expressions Unit Test
3 of 153 of 15 Items
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. Let's first simplify the constant terms:
\[
3 - 6 = -3
\]

3. For the \(r\) terms, we need a common denominator to combine \(-\frac{3}{4}r\) and \(-\frac{5}{6}r\). The least common multiple of 4 and 6 is 12.

Converting each term:
\[
-\frac{3}{4}r = -\frac{3 \times 3}{4 \times 3}r = -\frac{9}{12}r
\]
\[
-\frac{5}{6}r = -\frac{5 \times 2}{6 \times 2}r = -\frac{10}{12}r
\]

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

5. Putting it all together, we have:
\[
-\frac{19}{12}r - 3
\]

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