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

1 Answer

Answer:

#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).