document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206735>Question 1206735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the inequality │2x - 3│≥ 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844353 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844353\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor shows a perfectly good standard formal algebraic solution.<br><BR>\n" );
document.write( "A very different method for solving the problem is often much easier than the standard algebraic method.<br><BR>\n" );
document.write( "The expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-a%29=b ALIGN=MIDDLE  ALT=\"abs%28x-a%29=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be interpreted as saying the difference between x and a is equal to b.  For example, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-5%29=3 ALIGN=MIDDLE  ALT=\"abs%28x-5%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > means the difference between x and 5 is 3; that means x is either 5+3=8 or 5-3=2.<br><BR>\n" );
document.write( "We can solve this problem using that method.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x-3%29%3E=1 ALIGN=MIDDLE  ALT=\"abs%282x-3%29%3E=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Divide everything by 2, because we need \"x\" to be by itself:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-1.5%29%3E=0.5 ALIGN=MIDDLE  ALT=\"abs%28x-1.5%29%3E=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "This absolute value inequality says that the difference between x and 1.5 is greater than or equal to 0.5.<br><BR>\n" );
document.write( "1.5-0.5=1, so the difference between x and 1.5 is greater than or equal to 0.5 if x is less than or equal to 1;<BR>\n" );
document.write( "1.5+0.5=2, so the difference between x and 1.5 is greater than or equal to 0.5 if x is greater than or equal to 2<br><BR>\n" );
document.write( "So the inequality is satisfied if x is either less than or equal to 1, or greater than or equal to 2.<br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=1 ALIGN=MIDDLE  ALT=\"x%3C=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=2 ALIGN=MIDDLE  ALT=\"x%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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