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------------------------------------------------ Simplify [tex]8 + 3[x - 2[x + 5(x + 3)]] [/tex].

A. [tex]-33x + 82[/tex]
B. [tex]33x - 82[/tex]
C. [tex]-33x - 82[/tex]

Let's simplify the expression step by step:

1. Start with the innermost expression:
[tex]\[
5(x + 3)
\][/tex]
Distribute the 5:
[tex]\[
5x + 15
\][/tex]

2. Substitute and simplify the next expression:
Substitute [tex]$5x + 15$[/tex] into the expression [tex]$2[x + 5(x + 3)]$[/tex]:
[tex]\[
2[x + (5x + 15)]
\][/tex]
Simplify inside the brackets first:
[tex]\[
2[x + 5x + 15] \rightarrow 2[6x + 15]
\][/tex]
Now distribute the 2:
[tex]\[
12x + 30
\][/tex]

3. Substitute into the outer expression:
Substitute [tex]$12x + 30$[/tex] into the expression [tex]$3[x - 2[x + 5(x + 3)]]$[/tex]:
[tex]\[
3[x - (12x + 30)]
\][/tex]
Simplify inside the brackets:
[tex]\[
3[x - 12x - 30] \rightarrow 3[-11x - 30]
\][/tex]
Now distribute the 3:
[tex]\[
-33x - 90
\][/tex]

4. Add the constant from the original expression:
Finally, add 8 to the expression:
[tex]\[
8 + (-33x - 90)
\][/tex]
Simplify:
[tex]\[
-33x - 90 + 8 \rightarrow -33x - 82
\][/tex]

The simplified expression is:
[tex]\[
-33x - 82
\][/tex]