Question

Determine whether the equation is an identity or whether it has no solution.
4​(aminus4​)equals8aminus​(4aplus16​)

Answer 1

To determine whether the equation \( 4(a - 4) = 8a - (4a + 16) \) is an identity or has no solution, we can simplify both sides step by step.

Starting with the left side:

\[
4(a - 4) = 4a - 16
\]

Now, simplifying the right side:

\[
8a - (4a + 16) = 8a - 4a - 16 = 4a - 16
\]

Now, we have:

\[
4a - 16 = 4a - 16
\]

Since both sides of the equation are identical, the equation is an identity. This means that it is true for all values of \( a \).

Thus, the original equation \( 4(a - 4) = 8a - (4a + 16) \) is an identity.