document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117844>Question 117844</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the following inequality: -4(x-3)+ 5 <= 3x-7  (<= means the line underneath)<BR>\n" );
document.write( "a.  find the solution set for x<BR>\n" );
document.write( "b.  verify answer by checking on value inside the solution set and one value outside the solution set<BR>\n" );
document.write( "c. How does the answer change in the above equation change if we change the <= to a =.\r<BR>\n" );
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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 #85945 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=85945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can work these using the rules you apply to equations ... with the exception that if you<BR>\n" );
document.write( "multiply or divide both sides by a negative quantity, you reverse the direction of the inequality<BR>\n" );
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document.write( "Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28x-3%29%2B+5+%3C=+3x-7 ALIGN=MIDDLE  ALT=\"-4%28x-3%29%2B+5+%3C=+3x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "a) Find the solution set:<BR>\n" );
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document.write( "First do the distributed multiplication on the left side by multiplying -4 times each of<BR>\n" );
document.write( "the two terms in the parentheses. The multiplication leads to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x+%2B+12+%2B+5+%3C=+3x+-+7 ALIGN=MIDDLE  ALT=\"-4x+%2B+12+%2B+5+%3C=+3x+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side combine the +12 and +5 to get +17. This reduces the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x+%2B+17+%3C=+3x+-+7 ALIGN=MIDDLE  ALT=\"-4x+%2B+17+%3C=+3x+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the +17 on the left side by subtracting 17 from both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4x+%3C=+3x+-24 ALIGN=MIDDLE  ALT=\"-4x+%3C=+3x+-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, get rid of the 3x on the right side by subtracting 3x from both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7x+%3C=+-24 ALIGN=MIDDLE  ALT=\"-7x+%3C=+-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "To solve for +x, divide both sides by -7, the multiplier of x. Don't forget that since you are<BR>\n" );
document.write( "dividing both sides by a negative quantity, you must reverse the direction of the inequality<BR>\n" );
document.write( "sign. The division by -7 reduces the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+%28-24%29%2F%28-7%29 ALIGN=MIDDLE  ALT=\"x+%3E=+%28-24%29%2F%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the division on the right side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=+24%2F7 ALIGN=MIDDLE  ALT=\"x+%3E=+24%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "x can be any value equal to or greater than +24/7<BR>\n" );
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document.write( "b) Check ... suppose we let x be zero ... a value that is less than 24/7. Since this is outside<BR>\n" );
document.write( "the solution set, the inequality should not be correct.<BR>\n" );
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document.write( "Start with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28x-3%29%2B+5+%3C=+3x-7 ALIGN=MIDDLE  ALT=\"-4%28x-3%29%2B+5+%3C=+3x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Setting x equal to zero results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28-3%29+%2B+5+%3C=+-7 ALIGN=MIDDLE  ALT=\"-4%28-3%29+%2B+5+%3C=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+%2B+5+%3C=+-7 ALIGN=MIDDLE  ALT=\"12+%2B+5+%3C=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17+%3C=+-7 ALIGN=MIDDLE  ALT=\"17+%3C=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is not true ... +17 is not less than or equal to -7. So this checks.<BR>\n" );
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document.write( "Now let's set x equal to +4. Because 4 is greater than 24/7, the inequality should work.<BR>\n" );
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document.write( "Start with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%28x-3%29%2B+5+%3C=+3x-7 ALIGN=MIDDLE  ALT=\"-4%28x-3%29%2B+5+%3C=+3x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute +4 for x and it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%284+-+3%29+%2B+5%3C=3%284%29+-+7 ALIGN=MIDDLE  ALT=\"-4%284+-+3%29+%2B+5%3C=3%284%29+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the terms in the parentheses to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%281%29+%2B+5%3C=3%284%29+-+7 ALIGN=MIDDLE  ALT=\"-4%281%29+%2B+5%3C=3%284%29+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the multiplications ... one on the left side and one on the right side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%2B+5%3C=12+-+7 ALIGN=MIDDLE  ALT=\"-4+%2B+5%3C=12+-+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Combine the terms on the left side and also combine the terms on the right side.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%3C=+5 ALIGN=MIDDLE  ALT=\"1+%3C=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is true because 5 is greater than 1. So the inequality works for 1 value of x that is <BR>\n" );
document.write( "greater than 24/7.<BR>\n" );
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document.write( "c) How does the answer change if the inequality/equal sign is changed to an = sign.<BR>\n" );
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document.write( "The only thing this does is to change the inequality sign to an equal sign in the answer. With <BR>\n" );
document.write( "the equal sign in the problem the answer is just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24%2F7 ALIGN=MIDDLE  ALT=\"x+=+24%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "Hope this helps you to better understand the process of solving inequalities.<BR>\n" );
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document.write( "  </SPAN>\n" );
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