Which algebraic expression is equivalent to this expression?

[tex]\[ 3(2x - 8) - 11x \][/tex]

A. [tex]\(-5x - 24\)[/tex]
B. [tex]\(-17x - 24\)[/tex]
C. [tex]\(-17x - 8\)[/tex]
D. [tex]\(-5x - 8\)[/tex]



Answer :

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 across the terms inside the parentheses:
[tex]\[ 3(2x - 8) = 3 \cdot 2x - 3 \cdot 8 = 6x - 24 \][/tex]

2. Combine this result with the remaining part of the original expression:
[tex]\[ (6x - 24) - 11x \][/tex]

3. Combine the [tex]\(x\)[/tex]-terms:
[tex]\[ 6x - 11x = -5x \][/tex]

4. Combine the constant terms:
[tex]\[ -5x - 24 \][/tex]

Therefore, the simplified expression is:
[tex]\[ -5x - 24 \][/tex]

So, the algebraic expression equivalent to [tex]\( 3(2x - 8) - 11x \)[/tex] is:
[tex]\[ \boxed{-5x - 24} \][/tex]

This matches with option A.