Question

Determine whether the equation is an identity or whether it has no solution.
3​(aminus5​)equals6aminus​(3aplus15​)

Answer 1

Let's simplify the equation step by step.

The given equation is:

\[
3(a - 5) = 6 - (3a + 15)
\]

First, distribute on the left side:

\[
3a - 15 = 6 - (3a + 15)
\]

Next, simplify the right side by distributing the negative sign:

\[
3a - 15 = 6 - 3a - 15
\]

Now, combine like terms on the right side:

\[
3a - 15 = 6 - 15 - 3a
\]
\[
3a - 15 = -9 - 3a
\]

Next, we'll move the \(3a\) from the right side to the left side by adding \(3a\) to both sides:

\[
3a + 3a - 15 = -9
\]
\[
6a - 15 = -9
\]

Now, we'll add \(15\) to both sides:

\[
6a = -9 + 15
\]
\[
6a = 6
\]

Finally, divide both sides by \(6\):

\[
a = 1
\]

The equation has one solution: \(a = 1\).

It is not an identity since it does not hold true for all values of \(a\).