Algebraic Expressions Unit Test

Question

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