To solve the expression [tex]\( (5 - 3 \times [(-6) \div (5 + 1) - 5] - [(5 + 6) - (-7 + 9) - (-2)]) \)[/tex], we will go through it step by step:
1. Calculate the expression inside the first set of brackets:
[tex]\[
(-6) \div (5 + 1)
\][/tex]
Let's simplify inside the parenthesis first:
[tex]\[
5 + 1 = 6
\][/tex]
Now perform the division:
[tex]\[
(-6) \div 6 = -1
\][/tex]
2. Subtract 5 from the result:
[tex]\[
-1 - 5 = -6
\][/tex]
3. Multiply by 3:
[tex]\[
3 \times (-6) = -18
\][/tex]
4. Calculate the expression inside the second set of brackets:
First, simplify the sub-expressions:
[tex]\[
(5 + 6) - (-7 + 9) - (-2)
\][/tex]
Perform the additions and subtractions within the nested parentheses:
[tex]\[
5 + 6 = 11
\][/tex]
[tex]\[
-7 + 9 = 2
\][/tex]
Now substitute back into the expression:
[tex]\[
11 - 2 - (-2)
\][/tex]
Handling the double negative, we get:
[tex]\[
11 - 2 + 2 = 11
\][/tex]
5. Combine all parts of the expression:
The overall expression now looks like this:
[tex]\[
5 - (-18) - 11
\][/tex]
Simplify by performing the subtraction:
[tex]\[
5 + 18 - 11 = 23 - 11 = 12
\][/tex]
In conclusion, the value of the expression [tex]\( (5 - 3 \times [(-6) \div (5 + 1) - 5] - [(5 + 6) - (-7 + 9) - (-2)]) \)[/tex] is [tex]\( 12 \)[/tex].
