To determine which algebraic expression is equivalent to the given expression [tex]\( 3(2x - 8) - 11x \)[/tex], let's simplify it step-by-step:
1. Distribute the 3 within the parentheses:
[tex]\[
3(2x - 8) - 11x
\][/tex]
[tex]\[
3 \cdot 2x + 3 \cdot (-8) - 11x
\][/tex]
[tex]\[
6x - 24 - 11x
\][/tex]
2. Combine like terms:
- Combine the [tex]\(6x\)[/tex] and [tex]\( -11x\)[/tex].
[tex]\[
6x - 11x - 24
\][/tex]
[tex]\[
(6 - 11)x - 24
\][/tex]
[tex]\[
-5x - 24
\][/tex]
The simplified expression is [tex]\(-5x - 24\)[/tex].
From the given options, the equivalent expression is:
A. [tex]\(-5x - 8\)[/tex]
B. [tex]\(-5x - 24\)[/tex]
C. [tex]\(-17x + 24\)[/tex]
D. [tex]\(-17x - 24\)[/tex]
Reviewing the options, the correct one is:
B. [tex]\(-5x - 24\)[/tex]
