Answer:
[tex]n-1[/tex]
Step-by-step explanation:
The amount of integers between [tex]a[/tex] and [tex]b[/tex] inclusive is always [tex]|a-b|-1[/tex].
This means the amount of integers Michael wrote is [tex]|(3)-(n+5)|-1=|-2-n|-1=|n+2|-1[/tex]. Because [tex]n+5>=3[/tex] , which gives [tex]n>=-2[/tex], [tex]n+2[/tex] is always non-negative. So, we can kick out the absolute value sign to get [tex]n+2-1=n-1[/tex].
So, he wrote [tex]\boxed{n-1}[/tex] integers and we're done!
