Question

The number a is a number less than -3. what is the range of possible values of 1/a squared​

Answer 1

Numbers less than 1/9.

Explanation:

We are given a number
`a` and that it is less than -3.

That is
`a<-3`.

What is the range of possibles for
`(1)/(a^2)`?

So if
`a<-3` then
`a^2>9`.

*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
`a^2>9`, then
`(1)/(a^2)<(1)/(9)`.

*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.