Answer :
To simplify the expression [tex]\(8 + 3[x - 2[x + 5(x + 3)]]\)[/tex], we will follow a step-by-step process:
1. Start with the innermost expression:
Inside the parentheses, we begin with the expression [tex]\(5(x + 3)\)[/tex]:
[tex]\[
5(x + 3) = 5x + 15
\][/tex]
2. Substitute this into the next level:
Replace [tex]\(5(x + 3)\)[/tex] in the expression with the simplified result:
[tex]\[
2[x + 5(x + 3)] = 2[x + 5x + 15] = 2(6x + 15)
\][/tex]
Simplify further:
[tex]\[
2(6x + 15) = 12x + 30
\][/tex]
3. Move to the next outer bracket:
Substitute back into the main part of the expression:
[tex]\[
3[x - 2(x + 5(x + 3))] = 3[x - (12x + 30)]
\][/tex]
Simplify inside the bracket:
[tex]\[
x - (12x + 30) = x - 12x - 30 = -11x - 30
\][/tex]
4. Apply the multiplication:
Simplify by distributing the 3:
[tex]\[
3(-11x - 30) = -33x - 90
\][/tex]
5. Combine everything:
Add the result to the original number:
[tex]\[
8 + (-33x - 90) = -33x - 90 + 8
\][/tex]
Simplify this final expression:
[tex]\[
-33x - 82
\][/tex]
Therefore, the simplified expression is [tex]\(-33x - 82\)[/tex].
1. Start with the innermost expression:
Inside the parentheses, we begin with the expression [tex]\(5(x + 3)\)[/tex]:
[tex]\[
5(x + 3) = 5x + 15
\][/tex]
2. Substitute this into the next level:
Replace [tex]\(5(x + 3)\)[/tex] in the expression with the simplified result:
[tex]\[
2[x + 5(x + 3)] = 2[x + 5x + 15] = 2(6x + 15)
\][/tex]
Simplify further:
[tex]\[
2(6x + 15) = 12x + 30
\][/tex]
3. Move to the next outer bracket:
Substitute back into the main part of the expression:
[tex]\[
3[x - 2(x + 5(x + 3))] = 3[x - (12x + 30)]
\][/tex]
Simplify inside the bracket:
[tex]\[
x - (12x + 30) = x - 12x - 30 = -11x - 30
\][/tex]
4. Apply the multiplication:
Simplify by distributing the 3:
[tex]\[
3(-11x - 30) = -33x - 90
\][/tex]
5. Combine everything:
Add the result to the original number:
[tex]\[
8 + (-33x - 90) = -33x - 90 + 8
\][/tex]
Simplify this final expression:
[tex]\[
-33x - 82
\][/tex]
Therefore, the simplified expression is [tex]\(-33x - 82\)[/tex].
