document.write( "Question 1011030: If k is a constant and 2x+5=3kx+5 for all values of x, what is the value of k? \n" ); document.write( "
Algebra.Com's Answer #626557 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"2x%2B5=3kx%2B5\"\r\n" );
document.write( "\r\n" );
document.write( "Subtract 5 from both sides\r\n" );
document.write( "\r\n" );
document.write( "2x=3kx\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 3x, which can only be\r\n" );
document.write( "done for non-zero values of x.\r\n" );
document.write( "\r\n" );
document.write( "\"2x%2F%283x%29=%283kx%29%2F%283x%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"2%2F3=k\"\r\n" );
document.write( "\r\n" );
document.write( "That's no doubt the desired value of k, but we must continue\r\n" );
document.write( "on to show that it is also true when x=0 and k=\"2%2F3\".\r\n" );
document.write( "\r\n" );
document.write( "So we investigate to see if it also holds true for x=0:\r\n" );
document.write( "\r\n" );
document.write( "When we replace k by \"2%2F3\" in \r\n" );
document.write( "\r\n" );
document.write( "\"2x%2B5=3kx%2B5\"\r\n" );
document.write( "\r\n" );
document.write( "we get \r\n" );
document.write( "\r\n" );
document.write( "\"2x%2B5=3%282%2F3%29x%2B5\"\r\n" );
document.write( "\r\n" );
document.write( "and when we substitute x=0\r\n" );
document.write( "\r\n" );
document.write( "\"2%280%29%2B5=3%282%2F3%29%280%29%2B5\"\r\n" );
document.write( "\r\n" );
document.write( "\"0%2B5=0%2B5\"\r\n" );
document.write( "\r\n" );
document.write( "\"5=5\"\r\n" );
document.write( "\r\n" );
document.write( "Now since we have shown that it also holds for x=0, \r\n" );
document.write( "it holds for ALL values of x.\r\n" );
document.write( "\r\n" );
document.write( "[To have a rigorous proof we needed to show that\r\n" );
document.write( "it also held for x=0]\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );