Question

Is this equation an identity?

–0.6n + 16.92 = 16.92 − 0.6n

Answer 1

To determine if the equation \(-0.6n + 16.92 = 16.92 - 0.6n\) is an identity, we can simplify both sides of the equation and see if they are equivalent for all values of \(n\).

Starting with the left-hand side (LHS):
\[
\text{LHS} = -0.6n + 16.92
\]

Now, simplifying the right-hand side (RHS):
\[
\text{RHS} = 16.92 - 0.6n
\]

Now observe that both sides have \(16.92\) as a constant term, and the variable terms are \(-0.6n\) on the LHS and \(-0.6n\) on the RHS.

We can rewrite the RHS:
\[
\text{RHS} = 16.92 - 0.6n
\]
This can also be seen as:
\[
\text{RHS} = 16.92 + (-0.6n)
\]

Since both the left and right sides simplify to:
\[
-0.6n + 16.92 \quad \text{and} \quad 16.92 - 0.6n
\]

Thus, both sides are equal:
\[
-0.6n + 16.92 = -0.6n + 16.92
\]

Since this equality holds for all values of \(n\), we conclude that the given equation is indeed an identity.

So, yes, the equation \(-0.6n + 16.92 = 16.92 - 0.6n\) is an identity.