To simplify the expression [tex]\((-27a + 90) \div (-3)\)[/tex], we will follow step-by-step algebraic operations.
1. Distribute the Division Across the Terms:
The expression involves dividing a binomial by a constant. We distribute the division to each term of the binomial separately:
[tex]\[
\frac{-27a + 90}{-3} = \frac{-27a}{-3} + \frac{90}{-3}
\][/tex]
2. Simplify Each Term Individually:
- For the first term, [tex]\(\frac{-27a}{-3}\)[/tex]:
[tex]\[
\frac{-27a}{-3} = 9a
\][/tex]
(Since [tex]\(-27 \div -3 = 9\)[/tex])
- For the second term, [tex]\(\frac{90}{-3}\)[/tex]:
[tex]\[
\frac{90}{-3} = -30
\][/tex]
(Since [tex]\(90 \div -3 = -30\)[/tex])
3. Combine the Simplified Terms:
Now, we combine the simplified terms:
[tex]\[
\frac{-27a}{-3} + \frac{90}{-3} = 9a - 30
\][/tex]
Therefore, the simplified expression is:
[tex]\[
9a - 30
\][/tex]
