Intuition on $E[YX\mid X] = E[Y\mid X] X$

Question

I don't know how to think of/prove this equation: $$E[YX\mid X] = E[Y\mid X]X$$

I tried when $X = 1$:

$$E[YX\mid X] = \Pr(YX = 1\mid X = 1)YX = 1 = \Pr(Y\mid X = 1)Y = E[Y\mid X]X$$

It might be wrong and I am not sure how to think of the equation generally.

Answer 1

Given $X$, $X$ is a constant, so you can pull it out of the expectation by the linearity of expectation.