How to solve this problem involving convolution of negative input to delta function

Question

How to solve this problem involving convolution of negative input to delta function $$ x(-t) \ast \delta(-t-t_0) $$ $\ast$ - stands for convolution and $\delta$ stand for - dirac - delta function

Answer 1

$$ x(-t) \ast \delta(-t-t_0) = x(-t) \ast \delta(t+t_0) = x(-t) \ast \delta(t-(-t_0)) \\ = x(-(t-(-t_0))) = x(-(t+t_0)). $$

First equality: $\delta$ is even. Second equality: small rewrite. Third equality: $f(t) \ast \delta(t-t_0) = f(t-t_0)$. Fourth equality: obvious rewrite.