SOLUTION: please help me solve the inequality in interval notation {{{ l1-2xl-1>=1/3}}} thanks note: the l's are absolute value symbols

Question 439095: please help me solve the inequality in interval notation

thanks
note: the l's are absolute value symbols
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
please help me solve the inequality in interval notation
l1-2xl-1>=1/3
..
rule for absolute values:
x>=0,then |x|=x
x<0, then |x|=-x
Since we do not know whether (1-2x) is positive or negative, we must solve for both possibilities.
..
For positive possibility:
1-2x-1>=1/3
-2x>=1/3
-6x>=1
-x>=1/6
multiply by (-1) and reverse the inequality sign
x<-1/6
..
For negative possibility:
-1+2x-1>=1/3
2x-2>=1/3
6x-6>=1
6x>=7
x>=7/6
Solution:
(-infinity,-1/6] U [7/6,infinity)
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