document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1014301>Question 1014301</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two times the difference between a number and eleven is less than or equal to seven times the sum of the number and four. Find the smallest number that will satisfy the inequality.\r<BR>\n" );
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document.write( "what i tried..<BR>\n" );
document.write( "2(n-11) less than or equal to sign 7(n+4)<BR>\n" );
document.write( "simplified to 50 less than or equal to 5n<BR>\n" );
document.write( "divided 5 by each side ended up with 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #630625 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=630625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you're on the right track.<BR>\n" );
document.write( "however, the result is n >= -10.<BR>\n" );
document.write( "here's why.\r<BR>\n" );
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document.write( "start with 2 * (n-11) <= 7 * (n+4)<BR>\n" );
document.write( "distribute the multiplication to get 2n - 22 <= 7n + 28<BR>\n" );
document.write( "subtract 7n from both sides of the equation and add 22 to both sides of the equation to get 2n - 7n <= 28 + 22<BR>\n" );
document.write( "combine like terms to get -5n <= 50\r<BR>\n" );
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document.write( "here's where the inequality gets flipped.\r<BR>\n" );
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document.write( "divide both sides of the inequality by -5 to get n >= 50/-5<BR>\n" );
document.write( "simplify to get n >= -10\r<BR>\n" );
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document.write( "when you multiply or divide both sides of an inequality by a negative number, the inequality gets reversed.\r<BR>\n" );
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document.write( "you have a > b.<BR>\n" );
document.write( "multiply both sides of this inequality by -1 and you get -a < -b.<BR>\n" );
document.write( "in numbers, you would get the following:<BR>\n" );
document.write( "9 > 5<BR>\n" );
document.write( "multiply both sides by -1 and you get -9 < -5.\r<BR>\n" );
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document.write( "the equality part remains the same.<BR>\n" );
document.write( "7 = 7<BR>\n" );
document.write( "multiply both sides of this equation by -1 and you get -7 = -7<BR>\n" );
document.write( "they are still equal to each other, only with different signs.\r<BR>\n" );
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document.write( "in your inequality, you had -5n <= 50<BR>\n" );
document.write( "division is a form of multiplication and the same rules apply.<BR>\n" );
document.write( "dividing by 5 is the same as multiplying by 1/5.<BR>\n" );
document.write( "when you divided by -5, the inequality changes.<BR>\n" );
document.write( "you wind up with n >= -10.\r<BR>\n" );
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document.write( "i confirmed the solution is correct by replacing n with -11, -10, -9.<BR>\n" );
document.write( "the results are what i expected.<BR>\n" );
document.write( "when n was -11, 2*(n-11) <= 7*(n+4) was false (not smaller or equal).<BR>\n" );
document.write( "when n was -10, 2*(n-11) <= 7*(n+4) was true (equal).<BR>\n" );
document.write( "when n was -9, 2*(n-11) <= 7*(n+4) was true (smaller)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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