document.write( "Question 113228: 9(2x)=(9 x 2)x
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Algebra.Com's Answer #82401 by Edwin McCravy(20077)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "9(2x)=(9 x 2)x\r\n" );
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document.write( "You are using an x for both an unknown and also for \r\n" );
document.write( "the multiplication sign.  That makes it confusing.\r\n" );
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document.write( "So I'll use an askerisk * to denote multiplication.\r\n" );
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document.write( "9(2x) then means 9*(2*x)\r\n" );
document.write( "(9 x 2)x then means (9*2)*x\r\n" );
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document.write( "So the equation you have is\r\n" );
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document.write( "9*(2*x) = (9*2)*x\r\n" );
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document.write( "You are comparing 9*(2*x) with (9*2)*x.\r\n" );
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document.write( "Suppose x represents 3. Then\r\n" );
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document.write( "9*(2*x) = (9*2)*x\r\n" );
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document.write( "means\r\n" );
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document.write( "9*(2*3) = (9*2)*3\r\n" );
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document.write( "The left side of 9*(2*3) = (9*2)*3 is done this way:\r\n" );
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document.write( "We start with 9*(2*3). Then we do what's in the \r\n" );
document.write( "parentheses first and change the (2*3) to (6). \r\n" );
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document.write( "That makes 9*(2*3) become 9*(6)\r\n" );
document.write( "Then 9*(6) means 9*6 which comes out 54\r\n" );
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document.write( "Now let's do the right side of 9*(2*3) = (9*2)*3:\r\n" );
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document.write( "Starting with (9*2)*3, we do what's in the parentheses \r\n" );
document.write( "first and change the (9*2) to (18). \r\n" );
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document.write( "That makes (9*2)*3 become (18)*3\r\n" );
document.write( "Then (18)*3 means 18*3 which also comes out to equal 54.\r\n" );
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document.write( "Therefore 9*(2*x) = (9*2)*x is a true whenever x = 3.\r\n" );
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document.write( "Let's pick another number for x to see if it is true\r\n" );
document.write( "when x is that number.  Suppose we pick 1 for x this\r\n" );
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document.write( "Then\r\n" );
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document.write( "9*(2*x) = (9*2)*x\r\n" );
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document.write( "means\r\n" );
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document.write( "9*(2*1) = (9*2)*1\r\n" );
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document.write( "The left side of 9*(2*1) = (9*2)*1 is done this way:\r\n" );
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document.write( "We start with 9*(2*1). Then we do what's in the \r\n" );
document.write( "parentheses first and change the (2*1) to (2). \r\n" );
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document.write( "That makes 9*(2*1) become 9*(2)\r\n" );
document.write( "Then 9*(2) means 9*2 which comes out 18\r\n" );
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document.write( "Now let's do the right side of 9*(2*1) = (9*2)*1:\r\n" );
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document.write( "Starting with (9*2)*1, we do what's in the parentheses \r\n" );
document.write( "first and change the (9*2) to (18). \r\n" );
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document.write( "That makes (9*2)*1 become (18)*1\r\n" );
document.write( "Then (18)*1 means 18*1 which also comes out to equal 18.\r\n" );
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document.write( "Therefore 9*(2*x) = (9*2)*x is a true whenever x = 1.\r\n" );
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document.write( "Let's pick another number for x to see if it is true\r\n" );
document.write( "when x is that number.  Suppose we pick 87 for x this\r\n" );
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document.write( "Then\r\n" );
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document.write( "9*(2*x) = (9*2)*x\r\n" );
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document.write( "means\r\n" );
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document.write( "9*(2*87) = (9*2)*87\r\n" );
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document.write( "The left side of 9*(2*87) = (9*2)*87 is done this way:\r\n" );
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document.write( "We start with 9*(2*87). Then we do what's in the \r\n" );
document.write( "parentheses first and change the (2*87) to (174). \r\n" );
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document.write( "That makes 9*(2*87) become 9*(174)\r\n" );
document.write( "Then 9*(174) means 9*174 which comes out 1566\r\n" );
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document.write( "Now let's do the right side of 9*(2*87) = (9*2)*87:\r\n" );
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document.write( "Starting with (9*2)*87, we do what's in the parentheses \r\n" );
document.write( "first and change the (9*2) to (18). \r\n" );
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document.write( "That makes (9*2)*87 become (18)*87\r\n" );
document.write( "Then (18)*87 means 18*87 which also comes out to equal 1566.\r\n" );
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document.write( "Therefore 9*(2*x) = (9*2)*x is a true whenever x = 87.\r\n" );
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document.write( "So 9*(2*x) = (9*2)*x\r\n" );
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document.write( "must be true no matter what number x is. \r\n" );
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document.write( "They both involve multiplying three quantities,\r\n" );
document.write( "9, 2 and x.\r\n" );
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document.write( "In 9*(2*x) the parentheses are ASSOCIATING the\r\n" );
document.write( "2 and the x together\r\n" );
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document.write( "In (9*2)*x the parentheses are ASSOCIATING the\r\n" );
document.write( "9 and the 2 together.\r\n" );
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document.write( "So it's the ASSOCIATIVE PRINCIPLE that is being\r\n" );
document.write( "demonstrated here.\r\n" );
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document.write( "Edwin
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