document.write( "Question 439095: please help me solve the inequality in interval notation
\n" ); document.write( "\"+l1-2xl-1%3E=1%2F3\"
\n" ); document.write( "thanks\r
\n" ); document.write( "\n" ); document.write( "note: the l's are absolute value symbols \n" ); document.write( "
Algebra.Com's Answer #303513 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
please help me solve the inequality in interval notation
\n" ); document.write( "l1-2xl-1>=1/3
\n" ); document.write( "..
\n" ); document.write( "rule for absolute values:
\n" ); document.write( "x>=0,then |x|=x
\n" ); document.write( "x<0, then |x|=-x
\n" ); document.write( "Since we do not know whether (1-2x) is positive or negative, we must solve for both possibilities.
\n" ); document.write( "..
\n" ); document.write( "For positive possibility:
\n" ); document.write( "1-2x-1>=1/3
\n" ); document.write( "-2x>=1/3
\n" ); document.write( "-6x>=1
\n" ); document.write( "-x>=1/6
\n" ); document.write( "multiply by (-1) and reverse the inequality sign
\n" ); document.write( "x<-1/6
\n" ); document.write( "..
\n" ); document.write( "For negative possibility:
\n" ); document.write( "-1+2x-1>=1/3
\n" ); document.write( "2x-2>=1/3
\n" ); document.write( "6x-6>=1
\n" ); document.write( "6x>=7
\n" ); document.write( "x>=7/6\r
\n" ); document.write( "\n" ); document.write( "Solution:
\n" ); document.write( "(-infinity,-1/6] U [7/6,infinity) \n" ); document.write( "
\n" );