Which of the following expressions is equivalent to 54−6⋅v

Question

?(1 point)
Responses

6(−9−v)
6 left parenthesis negative 9 minus v right parenthesis

6(9+v)
6 left parenthesis 9 plus v right parenthesis

6(v−9)
6 left parenthesis v minus 9 right parenthesis

6(9−v)

Answer 1

To determine which expression is equivalent to \( 54 - 6 \cdot v \), we can factor out the common factor of 6 from the original expression.

Starting with:

\[ 54 - 6v \]

We can rewrite 54 as \( 6 \cdot 9 \):

\[ 54 - 6v = 6 \cdot 9 - 6v \]

Now we can factor out the 6:

\[ = 6(9 - v) \]

Now, let's check which of the responses is equivalent to this expression:

1. \( 6(-9 - v) \) = Not equivalent.
2. \( 6(9 + v) \) = Not equivalent.
3. \( 6(v - 9) \) = Not equivalent.
4. \( 6(9 - v) \) = Equivalent.

So the correct response is:

6(9−v).