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Simplify the following expression:
[tex]\[ 7 + \left( -2 + \left[ 5 + 4(-3) + (-6 + 2) + (-3) \right] \right) \][/tex]

Sagot :

GinnyAnsweridn
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]
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