Solve absolute value inequality. |5x-2|>13

William Boggs

William Boggs

Answered question

2021-12-07

Solve absolute value inequality.
|5x-2|>13

Answer & Explanation

censoratojk

censoratojk

Beginner2021-12-08Added 46 answers

Step 1
We have to solve the absolute value inequality:
|5x-2|>13
Case first:
When (5x2)>0x>25
then |5x-2|=(5x-2)
therefore,
|5x-2|>13
(5x-2)>13
5x-2+2>13+2
5x>15
5x5>155
x>3
Hence, solution set in this case is x>3 or x(3,).
Step 2
Case second:
When (5x2)<0x<25
then |5x-2|=-(5x-2)
Therefore,
|5x-2|>13
-(5x-2)>13
-5x+2>13
-5x+2-2>13-2
-5x>11
5x<-11 (inequality get changed when we multiply by negative quantity)
x<115
x<-2.2
So solution in this case is x<-2.2 or x(,2.2).
Finding solution from both case:
x>3 and x<-2.2
Hence, solution is x(,2.2)(3,).

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