Solve the inequality |x-4| > 8

Question

Solve the inequality |x-4| > 8

Answer 1

|x-4| > 8

 

The distance of x from 4 is more than 8.

 

<=====O-------------------+--------------------O=====>

             -4                         4                         12

 

x < -4 or x > 12

Answer 2

when solving problems with absolute value you must consider two cases

 

Case 1:   x-4 is positive

 

x-4>8

 

x> 12 This is one part of the solution

 

and

 

Case 2:  (x-4) is negative

 

-(x-4)>8

 

-x + 4 > 8

 

-x > 8-4

 

-x > 4

 

x < -4   we must change the order of the inequality when we divide by negtive 1

 

x < -4 this is the other part of the solution