Answer :
We begin with the expression
[tex]$$
8 + 3\Bigl[x - 2\Bigl(x + 5(x+3)\Bigr)\Bigr].
$$[/tex]
Step 1. Simplify the innermost bracket
Inside the square brackets, first simplify
[tex]$$
x + 5(x+3).
$$[/tex]
Distribute the [tex]$5$[/tex]:
[tex]$$
x + 5(x+3) = x + 5x + 15.
$$[/tex]
Combine like terms:
[tex]$$
x + 5x + 15 = 6x + 15.
$$[/tex]
Step 2. Simplify the next bracket
Now substitute back into the expression:
[tex]$$
x - 2(6x + 15).
$$[/tex]
Distribute the [tex]$-2$[/tex]:
[tex]$$
x - 12x - 30.
$$[/tex]
Combine like terms:
[tex]$$
x - 12x - 30 = -11x - 30.
$$[/tex]
Step 3. Multiply by [tex]$3$[/tex]
Returning to the full expression, multiply the bracket by [tex]$3$[/tex]:
[tex]$$
3(-11x - 30) = -33x - 90.
$$[/tex]
Step 4. Add the constant outside the bracket
Finally, add [tex]$8$[/tex]:
[tex]$$
-33x - 90 + 8 = -33x - 82.
$$[/tex]
Thus, the simplified expression is
[tex]$$
-33x - 82.
$$[/tex]
[tex]$$
8 + 3\Bigl[x - 2\Bigl(x + 5(x+3)\Bigr)\Bigr].
$$[/tex]
Step 1. Simplify the innermost bracket
Inside the square brackets, first simplify
[tex]$$
x + 5(x+3).
$$[/tex]
Distribute the [tex]$5$[/tex]:
[tex]$$
x + 5(x+3) = x + 5x + 15.
$$[/tex]
Combine like terms:
[tex]$$
x + 5x + 15 = 6x + 15.
$$[/tex]
Step 2. Simplify the next bracket
Now substitute back into the expression:
[tex]$$
x - 2(6x + 15).
$$[/tex]
Distribute the [tex]$-2$[/tex]:
[tex]$$
x - 12x - 30.
$$[/tex]
Combine like terms:
[tex]$$
x - 12x - 30 = -11x - 30.
$$[/tex]
Step 3. Multiply by [tex]$3$[/tex]
Returning to the full expression, multiply the bracket by [tex]$3$[/tex]:
[tex]$$
3(-11x - 30) = -33x - 90.
$$[/tex]
Step 4. Add the constant outside the bracket
Finally, add [tex]$8$[/tex]:
[tex]$$
-33x - 90 + 8 = -33x - 82.
$$[/tex]
Thus, the simplified expression is
[tex]$$
-33x - 82.
$$[/tex]
