document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77017>Question 77017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7(x – 3) > 5x - 14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55232 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=55232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 7(x – 3) > 5x - 14<BR>\n" );
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document.write( "The object of solving an inequality is to solve for x.<BR>\n" );
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document.write( "You can treat these problems about the same as an equation with one exception.  That <BR>\n" );
document.write( "exception is that if you divide or multiply both sides of the inequality by a negative<BR>\n" );
document.write( "number, then you must reverse the direction of the inequality arrow.<BR>\n" );
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document.write( "Let's proceed.  First multiply out the left side to get:<BR>\n" );
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document.write( "7x - 21 > 5x - 14<BR>\n" );
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document.write( "Get rid of the -21 on the left side of the equation by adding +21.  But if you add + 21 to<BR>\n" );
document.write( "the left side you must also add +21 to the right side.  When you do that, the inequality<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "7x > 5x + 7<BR>\n" );
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document.write( "(The +7 comes from -14 + 21.)<BR>\n" );
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document.write( "Now eliminate the 5x on the right side by subtracting 5x from it.  But when you subtract<BR>\n" );
document.write( "5x from the right side, you must also subtract it from the left side.  This causes<BR>\n" );
document.write( "the inequality to become:<BR>\n" );
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document.write( "2x > +7<BR>\n" );
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document.write( "Finally, divide both sides by 2 to solve for +x.  That division causes the inequality<BR>\n" );
document.write( "to become<BR>\n" );
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document.write( "x > +7/2 or x > +3.5<BR>\n" );
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document.write( "So x must lie to the right of 3.5 on the number line.  <BR>\n" );
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document.write( "Let's spot check.  Suppose we let x = +4. Plug that into the original problem and you<BR>\n" );
document.write( "get:<BR>\n" );
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document.write( "7(4 – 3) > 5*4 - 14<BR>\n" );
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document.write( "This simplifies to:<BR>\n" );
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document.write( "7(1) > 20 - 14<BR>\n" );
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document.write( "Which further simplifies to:<BR>\n" );
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document.write( "7 > 6<BR>\n" );
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document.write( "That works.  Now suppose we let x be a number less that 3.5 ... say x = 3. Plug that<BR>\n" );
document.write( "value into the original problem and it becomes:<BR>\n" );
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document.write( "7(3 – 3) > 5*3 - 14<BR>\n" );
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document.write( "which simplifies to:<BR>\n" );
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document.write( "0 > 15 - 14 or 0 > 1<BR>\n" );
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document.write( "that does NOT work.  So from these couple of spot checks, it appears that our solution<BR>\n" );
document.write( "is probably correct. (It is correct ...)<BR>\n" );
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document.write( "Hope this helps you to understand inequalities a little better, and helps you to see that<BR>\n" );
document.write( "for the most part you can operate on them just as you would an equation. And don't forget<BR>\n" );
document.write( "the rule that if you multiply or divide both sides of an inequality by a negative <BR>\n" );
document.write( "quantity, you must reverse the direction of the inequality arrow.  We did not need to <BR>\n" );
document.write( "apply that rule in this problem.<BR>\n" );
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