Sure, let's break down the expression step-by-step to solve it:
Given expression:
[tex]\[7 + (-2 + [5 + 4(-3) + (-6 + 2) + (-3)])\][/tex]
1. Start with the innermost parentheses:
[tex]\[ 4(-3) \][/tex]
[tex]\[ 4 \times (-3) = -12 \][/tex]
2. Next, evaluate the expression within the brackets:
[tex]\[ -6 + 2 \][/tex]
[tex]\[ -6 + 2 = -4 \][/tex]
3. Now substitute these results back into the original expression within the square brackets:
[tex]\[ 5 + 4(-3) + (-6 + 2) + (-3)\][/tex]
[tex]\[ 5 + (-12) + (-4) + (-3) \][/tex]
4. Sum the values inside the square brackets:
[tex]\[ 5 + (-12) + (-4) + (-3) = -14 \][/tex]
5. Next, substitute this result back into the whole expression:
[tex]\[ 7 + (-2 + [-14]) \][/tex]
6. Add the result from inside the square brackets to -2:
[tex]\[ -2 + (-14) = -16 \][/tex]
7. Finally, add this result to 7:
[tex]\[ 7 + (-16) = -9 \][/tex]
So, the final result of the given expression is:
[tex]\[ -9 \][/tex]
