document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=8485>Question 8485</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am confused concerning inequalities involving absolute value. Could you help me with the problem |3x+7|<7? <BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4702 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=4702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When you see an inequality of this form, you must split it into 2 different inequalities - one being exactly what you have, (Case I) except take out the absolute value signs, and the other, (Case II) also taking out the absolute value signs, however, altering the signs of the terms that were inside the absolute value.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case I - Problem as is - just take out the absolute value signs:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%2B+7+%3C+7+ ALIGN=MIDDLE  ALT=\"+3x+%2B+7+%3C+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <------ You'd solve this as if the < were an = sign, except, keep in mind that it really is a </\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3x+%3C+0+ ALIGN=MIDDLE  ALT=\"+3x+%3C+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- subtract 7 from both sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C+0+ ALIGN=MIDDLE  ALT=\"+x+%3C+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- divide by 3 on both sides.<BR>\n" );
document.write( "--------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case II - Flip the signs of the terms inside absolute value; get rid of absolute value\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3x+-+7+%3C+7+ ALIGN=MIDDLE  ALT=\"+-3x+-+7+%3C+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <-------- Start here\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3x+%3C+14+ ALIGN=MIDDLE  ALT=\"+-3x+%3C+14+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <------- Add 7 to both sides\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E+-14%2F3+ ALIGN=MIDDLE  ALT=\"+x+%3E+-14%2F3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <------ Divide by -3 on both sides. Notice that the direction of your inequality CHANGED. This is due to dividing both sides by a negative number. It's a rule to flip inequality when you divide (or multiply) by a negative number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So your answer is x > -14/3 and x < 0. Actually, when you put those together it's -14/3 < x < 0 because x lies between -14/3 and 0, but does not include those two values. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );