Which of the following is equivalent to the expression 8 - 2(3x - 4) + 5x? — Armed Services Vocational Aptitude Battery (ASVAB)

Which of the following is equivalent to the expression $8 - 2(3x - 4) + 5x$ ?

$-x + 16$ Answer
B
$23x - 24$
C
$-x$
D
$7x + 8$

Answer

The correct simplified expression is

-x + 16

The expression correctly applies the distributive property and the rules for combining like terms. Distributing

-2

into

(3x - 4)

yields

-6x + 8

. Combining the constants (

8 + 8

) gives

16

, and combining the variable terms (

-6x + 5x

) gives

-x

Step-by-Step Solution

Distribute the

-2

to the terms inside the parentheses.

8 - 6x + 8 + 5x

According to the order of operations (PEMDAS), the multiplication involved in the distributive property must be performed before addition and subtraction.

Group the like terms together.

(-6x + 5x) + (8 + 8)

Only terms with the same variable configuration (or constants) can be added or subtracted together.

Combine the like terms.

-x + 16

Adding the coefficients of the variable terms (

-6 + 5 = -1

) and adding the constants (

8 + 8 = 16

) yields the fully simplified expression.

Key Concept

Simplifying Algebraic Expressions

Question

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Step-by-Step Solution

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