Question

How are the solution sets to s<3 and |s|<3 different ?

Answer 1

The solution set for
`s<3` would be (-∞,3)

The solution set for
`|s|<3` would be (-3,3)

Explanation:

The solution set for
`s<3` can be any number that is lower than 3.

When we have the inequality
`|s|<3`, we need to rewrite this without the absolute values to find our answer

`|s|<3`

`s<` ±
`3`

This can be be split into
`s<3, s<-3`

But, there one thing that needs to be done to the inequality with the-3. As we multiplied it by a -1 to make it negative, we must reverse the sign of the inequality. This leaves us with
`s<3, s>-3`

Now, we can combine these to get one inequality

`-3<s<3`