College

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]

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]