Sure! Let's break down and simplify the given expression step by step.
The expression is:
[tex]\[5-3+(8+5)-\{-2+[c-5-2)+(12 \div 2)+4\}\][/tex]
1. Simplify within the first set of parentheses:
[tex]\[8+5 = 13\][/tex]
So, the expression now looks like:
[tex]\[5-3+13-\{-2+[c-5-2)+(12 \div 2)+4\}\][/tex]
2. Simplify within the brackets inside the braces:
[tex]\[c-5-2\][/tex]
First, combine [tex]\(-5\)[/tex] and [tex]\(-2\)[/tex]:
[tex]\[c - (5 + 2) = c - 7\][/tex]
So, the expression now is:
[tex]\[5-3+13-\{-2+[c-7)+(12 \div 2)+4\}\][/tex]
3. Simplify the division inside the brackets:
[tex]\[12 \div 2 = 6\][/tex]
So, the expression now is:
[tex]\[5-3+13-\{-2+[c-7]+6+4\}\][/tex]
4. Combine terms inside the brackets:
First, combine [tex]\[(c-7)\][/tex] and [tex]\[(6+4)\][/tex]:
[tex]\[c - 7 + 6 + 4\][/tex]
Simplify [tex]\(6 + 4\)[/tex]:
[tex]\[c - 7 + 10\][/tex]
[tex]\[c + 3\][/tex]
So, the expression now is:
[tex]\[5-3+13-\{-2+[c+3]\}\][/tex]
5. Simplify the brackets:
Replace [tex]\([c+3]\)[/tex] as [tex]\(c+3\)[/tex]:
[tex]\[5-3+13-\{-2+c+3\}\][/tex]
6. Simplify within the braces:
Combine [tex]\(-2\)[/tex] and [tex]\(3\)[/tex]:
[tex]\[-2 + 3 = 1\][/tex]
So, we get:
[tex]\[5-3+13-\{c+1\}\][/tex]
7. Remove the braces:
Since the braces enclose [tex]\(c+1\)[/tex], we keep the expression as:
[tex]\[5-3+13-(c+1)\][/tex]
8. Simplify the outer part:
First, simplify [tex]\(5-3\)[/tex]:
[tex]\[2\][/tex]
Add [tex]\(13\)[/tex]:
[tex]\[2 + 13 = 15\][/tex]
So now we have:
[tex]\[15 - (c + 1)\][/tex]
9. Simplify the final expression:
Distribute the subtraction:
[tex]\[15 - c - 1\][/tex]
Finally, combining constants:
[tex]\[15 - 1 = 14\][/tex]
So, the final simplified expression is:
[tex]\[14 - c\][/tex]
