Answer :
Let's simplify the expression step by step:
We start with the expression:
[tex]\[ 8 + 3(x - 2[x + 5(x + 3)]) \][/tex]
1. Innermost Parentheses: Simplify inside the innermost parentheses first, which is [tex]\(x + 3\)[/tex].
2. Multiplication Inside Brackets: Multiply 5 by the result of [tex]\(x + 3\)[/tex].
[tex]\[
5(x + 3) = 5x + 15
\][/tex]
3. Simplify the Brackets: Substitute back into the brackets.
[tex]\[
x + 5(x + 3) = x + 5x + 15 = 6x + 15
\][/tex]
4. Multiply by 2 Inside Parentheses: Multiply everything inside the parentheses by 2.
[tex]\[
2(6x + 15) = 12x + 30
\][/tex]
5. Simplify the Parentheses: Now substitute back and simplify inside the parentheses.
[tex]\[
x - (12x + 30) = x - 12x - 30 = -11x - 30
\][/tex]
6. Multiplication Outside Parentheses: Multiply the result by 3.
[tex]\[
3(-11x - 30) = -33x - 90
\][/tex]
7. Final Simplification with Addition: Add 8 to the result.
[tex]\[
8 + (-33x - 90) = -33x - 90 + 8 = -33x - 82
\][/tex]
After completing these steps, the simplified expression is:
[tex]\[ -33x - 82 \][/tex]
This matches one of the given choices: [tex]\(-33x - 82\)[/tex].
We start with the expression:
[tex]\[ 8 + 3(x - 2[x + 5(x + 3)]) \][/tex]
1. Innermost Parentheses: Simplify inside the innermost parentheses first, which is [tex]\(x + 3\)[/tex].
2. Multiplication Inside Brackets: Multiply 5 by the result of [tex]\(x + 3\)[/tex].
[tex]\[
5(x + 3) = 5x + 15
\][/tex]
3. Simplify the Brackets: Substitute back into the brackets.
[tex]\[
x + 5(x + 3) = x + 5x + 15 = 6x + 15
\][/tex]
4. Multiply by 2 Inside Parentheses: Multiply everything inside the parentheses by 2.
[tex]\[
2(6x + 15) = 12x + 30
\][/tex]
5. Simplify the Parentheses: Now substitute back and simplify inside the parentheses.
[tex]\[
x - (12x + 30) = x - 12x - 30 = -11x - 30
\][/tex]
6. Multiplication Outside Parentheses: Multiply the result by 3.
[tex]\[
3(-11x - 30) = -33x - 90
\][/tex]
7. Final Simplification with Addition: Add 8 to the result.
[tex]\[
8 + (-33x - 90) = -33x - 90 + 8 = -33x - 82
\][/tex]
After completing these steps, the simplified expression is:
[tex]\[ -33x - 82 \][/tex]
This matches one of the given choices: [tex]\(-33x - 82\)[/tex].
