Are these hypothese valid for a hypothesis test?

Question

In my textbook there is a question with the following hypotheses. $H$₀ $: \mu + 5 = 175$, with $H$₁: $\mu + 5 > 175$, now my question is, are these valid hypotheses and if so, are they identical to saying the following: $H$₀ $: \mu = 170$ and $H$₁ $: \mu > 170$, I am merely confused about this only because every other hypothesis test I've done is of the form $H$₀ $: \mu = k$, with one of the following, $H$₁ $: \mu > k $ , $H$₁ $: \mu < k $ or $H$₁ $: \mu ≠k $ .

Answer 1

Yes it is exactly the same (with my edit, you had put 175 when I think you meant 170). You can subtract 5 from both sides.