Question

Write the solution as either the union or intersection of two sets.
2│x-7│>28

Answer 1

hello,

so we can divide both sides by 2:
|x-7| > 14

now we will check for what x's the next equation holds:
|x-7| = 14

now we have two options :
1. x-7 = 14
or
2. x-7 = -14

so 1.
x = 21
2.
x = -7

now we have found the values for |x-7|=14 but we want |x-7|>14

so we sketch:

Answer 2

for example, for the x<-7 part we can choose x = -10
plug it into the inequality
|-10-7| = -17
and it is >14

so it is good for us.

for the -7<x<21 we can choose x =0
|0-7| = 7
and it is < 14
so it is not good for us either.

we left with x>21
we choose 22
|22 - 7| = 15
is it >14
and it is good for us


so the solution is

x>21 or x<-7 ( union)