Question

Is this equation an identity?

6(–2v − 3) = –12v

Answer 1

To determine if the equation \( 6(-2v - 3) = -12v \) is an identity, we need to simplify the left-hand side and see if it equals the right-hand side for all values of \( v \).

Start by simplifying the left side:

\[
6(-2v - 3) = 6 \cdot (-2v) + 6 \cdot (-3)
\]
\[
= -12v - 18
\]

Now the equation becomes:

\[
-12v - 18 = -12v
\]

Next, isolate the terms involving \( v \):

Subtract \( -12v \) from both sides:

\[
-18 = 0
\]

This results in a contradiction. The equation \( -18 = 0 \) is false.

Since the left-hand side simplifies to something that does not equal the right-hand side for all values of \( v \), the equation

\[
6(-2v - 3) = -12v
\]

is not an identity.