Question

How do you solve and graph `abs(9-x)>21`?

Answer 1

`x<-12, x>30`

Explanation:

Remember that the absolute value sign will always return a negative, so that, for instance where we have `absx=3`, `x` can be 3 but it can also be `-3`. And so we need to look at the positive and negative values that can be inside the absolute value sign.

Positive

`9-x>21`

`-x>12`

`x<-12`

Negative

`-(9-x)>21`

`-9+x>21`

`x>30`

Put it together and we have:

`x<-12, x>30`

To graph this, place hollow circles around `-12` and 30 to indicate that they are not part of the solution. Then draw rays heading away from the origin (the ray from `-12` points towards larger negative values while the ray from 30 points towards larger positive values).