Let's simplify the expression [tex]\(25 - 5 + \frac{36}{9} - 6 \cdot 7\)[/tex] step by step, following the order of operations (PEMDAS/BODMAS rules: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition, and Subtraction (from left to right)).
1. First, we handle any operations within parentheses. There are no parentheses that alter the operations inside them in this expression, so we proceed to the multiplication and division from left to right.
2. We start with the division [tex]\(\frac{36}{9}\)[/tex]:
[tex]\[
\frac{36}{9} = 4
\][/tex]
Now, the expression becomes:
[tex]\[
25 - 5 + 4 - 6 \cdot 7
\][/tex]
3. Next, we handle the multiplication [tex]\(6 \cdot 7\)[/tex]:
[tex]\[
6 \cdot 7 = 42
\][/tex]
Now, the expression becomes:
[tex]\[
25 - 5 + 4 - 42
\][/tex]
4. Now, we proceed with addition and subtraction from left to right. First, subtract 5 from 25:
[tex]\[
25 - 5 = 20
\][/tex]
Now, the expression becomes:
[tex]\[
20 + 4 - 42
\][/tex]
5. Next, add 4 to 20:
[tex]\[
20 + 4 = 24
\][/tex]
Now, the expression becomes:
[tex]\[
24 - 42
\][/tex]
6. Finally, perform the subtraction [tex]\(24 - 42\)[/tex]:
[tex]\[
24 - 42 = -18
\][/tex]
Thus, the simplified result of the expression [tex]\(25 - 5 + \frac{36}{9} - 6 \cdot 7\)[/tex] is [tex]\(\boxed{-18}\)[/tex].
