document.write( "Question 215084:
\n" ); document.write( " If \"5%3Ca%3C7\"\"%22%22%3Cb%3C14\",then prove that \"5%2F14%3Ca%2Fb%3C1\"
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #162539 by Edwin McCravy(20067)\"\" \"About 
You can put this solution on YOUR website!
If \"5%3Ca%3C7\"\"%22%22%3Cb%3C14\" then prove that \"5%2F14%3Ca%2Fb%3C1\"
\n" ); document.write( "
\r\n" );
document.write( "\"b%3C14\" is given\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by \"1%2F%2814b%29\" which is positive and\r\n" );
document.write( "does not reverse inequality:\r\n" );
document.write( "\r\n" );
document.write( "\"b%281%2F%2814b%29%29%3C14%2F%2814b%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"cross%28b%29%281%2F%2814cross%28b%29%29%29%3Ccross%2814%29%2F%28cross%2814%29b%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"1%2F14+%3C+1%2Fb\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by \"a\" which is positive and does\r\n" );
document.write( "not reverse the inequality:\r\n" );
document.write( "\r\n" );
document.write( "(1)       \"a%2F14%3Ca%2Fb\"\r\n" );
document.write( "\r\n" );
document.write( "\"5%3Ca\" is given\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by \"1%2F14\"\r\n" );
document.write( "\r\n" );
document.write( "(2)      \"5%2F14%3Ca%2F14\"\r\n" );
document.write( "\r\n" );
document.write( "By inequalities (1) and (2),\r\n" );
document.write( "\r\n" );
document.write( "\"5%2F14%3Ca%2F14%3Ca%2Fb\"\r\n" );
document.write( "\r\n" );
document.write( "So \r\n" );
document.write( "\r\n" );
document.write( "(3)  \"5%2F14%3Ca%2Fb\"\r\n" );
document.write( "\r\n" );
document.write( "Now we only need show that \"a%2Fb%3C1\"\r\n" );
document.write( "\r\n" );
document.write( "We are given that \"a%3C7%3Cb\" so\r\n" );
document.write( "\r\n" );
document.write( "\"a%3Cb\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by \"1%2Fb\"\r\n" );
document.write( "\r\n" );
document.write( "\"a%2Fb%3Cb%2Fb\"\r\n" );
document.write( "\r\n" );
document.write( "(4)  \"a%2Fb%3C1\"\r\n" );
document.write( "\r\n" );
document.write( "By (3) and (4),\r\n" );
document.write( "\r\n" );
document.write( "\"5%2F14+%3C+a%2Fb+%3C+1\"\r\n" );
document.write( "\r\n" );
document.write( "which was to be proved.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );