Select the correct answer.

Which algebraic expression is equivalent to this expression?
[tex]$3(2 x-8)-11 x$[/tex]
A. [tex]$-5 x-8$[/tex]
B. [tex]$-17 x-24$[/tex]
C. [tex]$-5 x-24$[/tex]
D. [tex]$-17 x+24$[/tex]

The problem requires simplifying the algebraic expression 3 ( 2 x − 8 ) − 11 x .

Distribute the constant: 3 ( 2 x − 8 ) = 6 x − 24 .
Rewrite the expression: 6 x − 24 − 11 x .
Combine like terms: − 5 x − 24 .
The equivalent expression is − 5 x − 24 ​ .

Explanation

Understanding the Problem We are given the expression 3 ( 2 x − 8 ) − 11 x and asked to find an equivalent algebraic expression from the given options.

Distributing the Constant First, we need to distribute the 3 across the terms inside the parenthesis: 3 ( 2 x − 8 ) = 3 × 2 x − 3 × 8 = 6 x − 24

Substituting Back Now, substitute this back into the original expression: 3 ( 2 x − 8 ) − 11 x = ( 6 x − 24 ) − 11 x

Combining Like Terms Next, we combine like terms. We have 6 x and − 11 x , which combine to give − 5 x . The constant term is − 24 . So, we have: 6 x − 24 − 11 x = ( 6 x − 11 x ) − 24 = − 5 x − 24

Finding the Correct Option Comparing our simplified expression − 5 x − 24 with the given options, we see that it matches option C.


Examples
Algebraic expressions are used to model real-world situations. For example, if a store is offering a discount of $3 on each item and a further 10% discount on the total purchase, the final price can be represented as an algebraic expression. Simplifying such expressions helps in calculating the final price efficiently.

Answered by GinnyAnswer | 2025-07-03

The equivalent algebraic expression for 3 ( 2 x − 8 ) − 11 x simplifies to − 5 x − 24 , which is option C. This was determined by distributing and combining like terms in the original expression. Therefore, the chosen option is C.
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Answered by Anonymous | 2025-07-04