Answer :

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]