document.write( "Question 258767: \"abs%283x+%2B+1%29+%2B+abs%283+-+2x%29+=+11\"
\n" ); document.write( "\"x+=+%22%3F%22\" \n" ); document.write( "
Algebra.Com's Answer #190496 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
Break up the number line into 3 distinct regions using the absolute value arguments.
\n" ); document.write( "3x+1=0
\n" ); document.write( "x=-1/3
\n" ); document.write( "When \"x%3C-1%2F3\", \"abs%283x+%2B+1%29=-%283x%2B1%29\"
\n" ); document.write( "When \"x%3E-1%2F3\", \"abs%283x+%2B+1%29=3x%2B1\"
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "3-2x=0
\n" ); document.write( "3=2x
\n" ); document.write( "x=3/2
\n" ); document.write( "When \"x%3C3%2F2\", \"abs%283-2x%29=3-2x\"
\n" ); document.write( "When \"x%3E3%2F2\",\"abs%283-2x%29=-%283-2x%29\"
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Here are the 3 regions.
\n" ); document.write( "(\"+-infinity\",\"-1%2F3\")
\n" ); document.write( "\"-%283x%2B1%29%2B%283-2x%29=11\"
\n" ); document.write( "\"-3x-1%2B3-2x=11\"
\n" ); document.write( "\"-5x%2B2=11\"
\n" ); document.write( "\"x=-9%2F5\"
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "(\"-1%2F3\",\"3%2F2\")
\n" ); document.write( "\"%283x%2B1%29%2B%283-2x%29=11\"
\n" ); document.write( "\"x%2B4=11\"
\n" ); document.write( "\"x=7\"
\n" ); document.write( "Not in the valid region, no solution.
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "(\"3%2F2\",\"infinity\")
\n" ); document.write( "\"%283x%2B1%29-%283-2x%29=11\"
\n" ); document.write( "\"3x%2B1-3%2B2x=11\"
\n" ); document.write( "\"5x-2=11\"
\n" ); document.write( "\"5x=13\"
\n" ); document.write( "\"x=13%2F5\"
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "Two solutions: x=-9/5 and x=13/5. \n" ); document.write( "
\n" );