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Solve the inequality |x-4| > 8

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2 Answers

|x-4| > 8
 
The distance of x from 4 is more than 8.
 
<=====O-------------------+--------------------O=====>
             -4                         4                         12
 
x < -4 or x > 12
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