An identity is an equation of the form:
x = x, 2 = 2, or something like that
So here, we want to find a value of a for the equation
8×x - 8 + 3×a×x = 5×a×x - 2×a
Such that we can reduce this to the identity form.
let's rewrite our equation, let's move all the terms with x to the left side and the terms without x to the right side.
8×x + 3×a×x - 5×a×x = 8 - 2×a
(8 +3×a - 5×a)×x = 8 - 2×a
A good form of making this an identity is removing x alltogether (this does not always work, but let's try it as our first attempt).
Then we must have:
8 +3×a - 5×a = 0
8 - 2×a = 0
8 = 2×a
8/2 = a = 4
Replacing that in our equation we get:
(8 +3×4 - 5×4)×x = 8 - 2×4
0×x = 0
0 = 0
So this is an identity, which means that the value of a that we must choose is a = 4.
If you want to learn more, you can read:
https://brainly.com/question/9435009
