Question

Item 6 for what value of a is 8x−8+3ax=5ax−2a an identity?

Answer 1

Let's rewrite the expression as

`8x+3ax-5ax = 8-2a \iff 8x - 2ax = 8-2a \iff 2x(4-a) = 2(4-a)`

So, if
`a \\eq 4`, you may divide both sides by
`4-a`, the equation becomes
`2x=2`, and the only solution is
`x=1`, which means that this is not an identity (an indentity is tautologically true, no matter the value of x).

If instead
`a = 4`, you are multiplying both sides by zero, so the equation becomes

`2x \cdot 0 = 2 \cdot 0 \iff 0=0`

So, it doesn't matter which value for x you choose, because you will always end up with
`0=0`, which is obviously always true.