Let's solve the expression step by step:
[tex]\[ 7 + (-2 + [5 + 4(-3) + (-6 + 2) + (-3)]) \][/tex]
1. Solve the innermost parentheses first:
[tex]\[
-6 + 2 = -4
\][/tex]
2. Substitute this result back into the expression:
[tex]\[
7 + (-2 + [5 + 4(-3) + (-4) + (-3)])
\][/tex]
3. Next, handle the multiplication inside the brackets:
[tex]\[
4(-3) = -12
\][/tex]
4. Substitute this result back:
[tex]\[
7 + (-2 + [5 + (-12) + (-4) + (-3)])
\][/tex]
5. Now, sum the numbers inside the brackets ([ ]):
[tex]\[
5 + (-12) + (-4) + (-3) = 5 - 12 - 4 - 3 = -14
\][/tex]
6. Substitute this result back:
[tex]\[
7 + (-2 + [-14])
\][/tex]
7. Resolve the inner most parentheses:
[tex]\[
-2 + (-14) = -16
\][/tex]
8. Finally, add this to 7:
[tex]\[
7 + (-16) = -9
\][/tex]
So, the value of the given expression is:
[tex]\[ \boxed{-9} \][/tex]
