document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76074>Question 76074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5-3x>56 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54617 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=54617\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5-3x%3E56 ALIGN=MIDDLE  ALT=\"5-3x%3E56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can operate on inequalities just as you would on an equation with one exception.<BR>\n" );
document.write( "That exception is that if you multiply or divide both sides of the inequality by a negative<BR>\n" );
document.write( "number, you need to reverse the direction of the inequality.<BR>\n" );
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document.write( "In the given problem we need to solve for +x.  To do this we will start by eliminating<BR>\n" );
document.write( "the 5 on the left side to leave only the term containing the x on the left side.  Eliminate<BR>\n" );
document.write( "the 5 on the left side by subtracting 5 from both sides.  When you do the inequality<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3x+%3E+56+-+5 ALIGN=MIDDLE  ALT=\"+-3x+%3E+56+-+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the two numbers that are now on the right side and the inequality is simplified<BR>\n" );
document.write( "to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-3x+%3E+51+ ALIGN=MIDDLE  ALT=\"+-3x+%3E+51+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To solve for +x divide both sides by -3.  Because you are dividing both sides by a minus<BR>\n" );
document.write( "number you need to reverse the direction of the inequality.  Both of these actions <BR>\n" );
document.write( "(dividing both sides by -3 and reversing the direction of the inequality sign) results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C+51%2F%28-3%29 ALIGN=MIDDLE  ALT=\"+x+%3C+51%2F%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and this simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C+-17 ALIGN=MIDDLE  ALT=\"+x+%3C+-17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This means that on a number line, x can only have values lying to the left of -17.<BR>\n" );
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document.write( "Check by letting x be some value less than -17.  For example, let x be -18. If you plug<BR>\n" );
document.write( "that value into the original problem in place of x you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+-+3%2A%28-18%29+%3E+56 ALIGN=MIDDLE  ALT=\"5+-+3%2A%28-18%29+%3E+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+54+%3E+56 ALIGN=MIDDLE  ALT=\"5+%2B+54+%3E+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is true so when x is less than -17 we have one supporting piece of evidence that it<BR>\n" );
document.write( "might be true.  Now let's try letting x = -16.  Substitute this into the original <BR>\n" );
document.write( "problem and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+-3%2A%28-16%29+%3E+56 ALIGN=MIDDLE  ALT=\"5+-3%2A%28-16%29+%3E+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The left side becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+48+%3E+56 ALIGN=MIDDLE  ALT=\"5+%2B+48+%3E+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can see that this is NOT true ... so when x is greater than -17 we have an example<BR>\n" );
document.write( "that says it will not work.<BR>\n" );
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document.write( "Hope that this helps you to understand a little more about how inequalities can be solved.\r<BR>\n" );
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