Can someone please explain this to me?

Givenf(n)=2n + 3 lg n, g(n)=n, prove that 2n + 3 lg n= Θ(n)

Proof:

•2n + 3 lg n ≤ 2n+3n = 5n for all n ≥ 1

•Hence, we can takek1=5, and n1=1, and conclude that f(n)= O(n)

•Since 2n + 3 lg n ≥ 2n, for all n ≥ 1,

•we can takek2= 2, and n2=1, and conclude that f(n) = Ω(n)

•Therefore, we have 2n + 3lgn = Θ(n)