document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209263>Question 1209263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a, b and c are integers. If a < b, then ac < bc. Is the statement true or false? </SPAN>\n" );
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document.write( "Answer: <font color=red>False</font>\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "We only need one counter-example to disprove this claim.<BR>\n" );
document.write( "This is because the claim encompasses all integers (and we can change \"integers\" to \"real numbers\" to get the same idea).\r<BR>\n" );
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document.write( "Let's say that,<BR>\n" );
document.write( "a = 1, b = 2, c = -3\r<BR>\n" );
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document.write( "a < b is true since 1 < 2 is true.<BR>\n" );
document.write( "However,<BR>\n" );
document.write( "a*c < b*c<BR>\n" );
document.write( "1*(-3) < 2*(-3)<BR>\n" );
document.write( "-3 < -6<BR>\n" );
document.write( "is false\r<BR>\n" );
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document.write( "Use a number line to see that -6 is to the left of -3, so -6 is actually the smaller item. <BR>\n" );
document.write( "A vertical number line could help paint a better picture. The -6 is further down compared to -3.\r<BR>\n" );
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document.write( "How to make the statement true? Simply mention \"c is positive\".  <BR>\n" );
document.write( "Incorrect: \"a < b leads to ac < bc\"<BR>\n" );
document.write( "Correct: \"If c is positive, then a < b leads to ac < bc\"\r<BR>\n" );
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document.write( "Or if you said \"if c is negative, then a < b leads to ac > bc\", it would be a true claim.<BR>\n" );
document.write( "I've seen many students forget to flip the inequality sign when multiplying both sides by a negative number.<BR>\n" );
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