Answer:
1.- For the first case we need the absolute value of x greater than 3, this is represented by:
|x|>3
and this has two solutions, one with the positive x and one with the negative x:
solutions to |x|>3:
+x>3
and -x>3 which is x<-3, so combining the two solutions we get:
3<x<-3, in the number line we are going to have two sections, one with the numbers that are greater than 3 and the other with the numbers less than -3 (as seen in the first number line of the attached image).
2.- for the second case we need the absolute of x less than 3, this is represented by:
|x|<3
this also has two solutions (one with the positive x and the other with the negative x)
solutions to |x|<3
x<3
and
-x<3 which is x>-3
combining these two solutions we get
-3<x<3
the number line for this is the second number line in the attached image.
