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Simplify the following expression:
[tex]\[9 - 4 - [63 - [(41 + 10 - 5) - (53 + 12)] - 91 + 11]\][/tex]

Sagot :

GinnyAnsweridn
Certainly! Let's solve the given expression step-by-step:

[tex]\[ 9 - 4 - [63 - [(41 + 10 - 5) - (53 + 12)] - 91 + 11] \][/tex]

### Step 1: Simplify innermost parentheses
First, handle the operations inside the innermost parentheses:

- [tex]\(41 + 10 - 5\)[/tex]:

[tex]\[41 + 10 = 51\][/tex]
[tex]\[51 - 5 = 46\][/tex]

So, [tex]\(41 + 10 - 5 = 46\)[/tex].

- [tex]\(53 + 12\)[/tex]:

[tex]\[53 + 12 = 65\][/tex]

Now we have:

[tex]\[9 - 4 - [63 - (46 - 65) - 91 + 11]\][/tex]

### Step 2: Simplify the inner subtraction
Next, simplify [tex]\(46 - 65\)[/tex]:

[tex]\[46 - 65 = -19\][/tex]

Now the expression becomes:

[tex]\[9 - 4 - [63 - (-19) - 91 + 11]\][/tex]

### Step 3: Handle the subtraction within the brackets
Simplify within the brackets:

[tex]\[63 - (-19) = 63 + 19 = 82\][/tex]

Now the expression becomes:

[tex]\[9 - 4 - [82 - 91 + 11]\][/tex]

### Step 4: Simplify further within the brackets
Continue simplifying:

[tex]\[82 - 91 = -9\][/tex]
[tex]\[-9 + 11 = 2\][/tex]

So now the expression is:

[tex]\[9 - 4 - 2\][/tex]

### Final Step: Simplify the outer expression
Finally, handle the remaining subtraction:

[tex]\[9 - 4 = 5\][/tex]
[tex]\[5 - 2 = 3\][/tex]

Thus, the result of the expression is:

[tex]\[ \boxed{3} \][/tex]
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