Question

How do you solve `9< | c + 7|`?

Answer 1

`c>2` or `c<-16`

Explanation:

Let's see it the other way: `|c+7|>9`. I think this is more helpful, because we know that if `|x|>\alpha`, then one between `x<-\alpha` and `x>\alpha` must hold.

So, in your case, we have two possibilities:

• `c+7>9`, which yields `c>2`

• `c+7<-9`, which yields `c<-16`

In other words, we want the quantity `c+7` to be, in an absolute sense, larger than `9`. This means that it has to be very large (`>9`), or very small (`<-9`), since the absolute always return the positive version of the number, and thus it is true that `|-25|>9`, because it means `25>9`.