Negation of formal statement of continuity

Question

I am asked to find the negation of $∀a ∈ R ∀ε > 0 ∃δ > 0 ∀x ∈ R, |x − a| < δ : |3x − 3a| < ε$

What I got is $∃a ∈ R ∃ε > 0 ∀δ > 0 ∃x ∈ R, |x − a| < δ : |3x − 3a| >= ε$, is this correct? Most of my doubt is about $∃x ∈ R$. Thanks!