Posted by Jenni on .
absolute value of(x + 3) + absolute value of (3  x) < 9.
I am not sure how to go about this question. Although, we generally use three cases.

math 
Reiny,
let's rewrite it as
x+3 < 9  3x
x+3 < 9  3x or x3 < 9  3x
3x < 6x , #1)
or
3x < 12 + x , (#2)
from #1
3x < 6x
no solution
or
3 + x < 6x
2x < 9
x < 9/2
from #2
3x < 12+x
2x < 9
x > 9/2
or
3+x < 12 +x
no solution
so we have x< 9/2 and x > 9/2
our critical values of 9/2 and +9/2 divide our number line into 3 parts
1. x < 9/s
2. x between 9/2 and 9/2
3. x > 9/2
I usually pick an arbitrary number in each region and test it in the original
1. let x = 10 > 7< 9 13 false
2. let x = 0 > 3 < 9  3 true
3. let x = 10 > 13 < 9  7 false
so 9/2 < x < 9/2 
math 
Jenni,
Thank You!