Question

On a number line show all values of x that..

Answer 1

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.