Answer:
Numbers less than 1/9.
Step-by-step explanation:
We are given a number [tex]a[/tex] and that it is less than -3.
That is [tex]a<-3[/tex].
What is the range of possibles for [tex]\frac{1}{a^2}[/tex]?
So if [tex]a<-3[/tex] then [tex]a^2>9[/tex].
*I knew to flip inequality here because if I square any number less than -3 it was going have a value bigger than 9.
If [tex]a^2>9[/tex], then [tex]\frac{1}{a^2}<\frac{1}{9}[/tex].
*When taking reciprocal flip the inequality.
Let's do a test:
Let's see if we pick a number less than -3 that we get a result that is less than 1/9 after we find the reciprocal of the square of the number we choose.
Let's pick -4.
-4 is less than -3
Square -4, you get 16 and 16>9.
The reciprocal of 16 is 1/16 and 1/16<1/9.
So 1/16 is a number less than 1/9.
