Question

Drag each expression to show whether it is equivalent to 54x 18 or (6⋅9x) (6⋅1).

a) clear check 18(3x 1)
b) 3(18x 2)
c) 54x 6
d) (6⋅9x) (6⋅3)

Answer 1

The goal is to identify if the provided expressions are equivalent to 54x + 18 or (6·9x) + (6·1). Expression a) 18(3x + 1) is equivalent to 54x + 18 while other expressions do not match the originals.

Step-by-step explanation:

The subject of the question pertains to the concept of algebraic expression equivalency, specifically determining if given expressions are equivalent to either 54x + 18 or (6·9x) + (6·1).

Here is a review of each expression:

• a) 18(3x + 1) is equivalent to 54x + 18 because when we distribute 18 to both terms inside the parentheses, we get 18·3x + 18·1 which simplifies to 54x + 18.
• b) 3(18x + 2) is not equivalent to either of the given expressions because when we distribute 3 to both terms inside the parentheses, we get 54x + 6, which does not match either of the original expressions.
• c) 54x + 6 is not equivalent to either of the given expressions because the constant term diverges from the other provided choices.
• d) (6·9x) + (6·3) is equivalent to (6·9x) + (6·1) except that the constant is different, showing that instead of a 1 there's a 3, hence it must be corrected to be equivalent.