document.write( "Question 1184616: Follow the steps given, make a conjecture then prove your conjecture deductively:\r
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Algebra.Com's Answer #815320 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "See what happens with 2\r\n" );
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document.write( "1. Think of a number. **I chose 2 pls**\r\n" );
document.write( "2. Multiply the number by 5.  **I get 10**\r\n" );
document.write( "3. Add 17 to the result in Step 2.  **I get 27**\r\n" );
document.write( "4. Triple the result in Step 3.     **I get 81**\r\n" );
document.write( "5. Reduce the result in Step 4 by 6  **I get 75**\r\n" );
document.write( "6. Divide the result in Step 5 by 5  **I get 15**\r\n" );
document.write( "7. Subtract 9 from the result in Step 6  **I get 6**\r\n" );
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document.write( "I notice that 6 is 3 times the 2 that I started with.\r\n" );
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document.write( "See what happens with 10\r\n" );
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document.write( "1. Think of a number. **I chose 10 pls**\r\n" );
document.write( "2. Multiply the number by 5.  **I get 50**\r\n" );
document.write( "3. Add 17 to the result in Step 2.  **I get 67**\r\n" );
document.write( "4. Triple the result in Step 3.     **I get 201**\r\n" );
document.write( "5. Reduce the result in Step 4 by 6  **I get 195**\r\n" );
document.write( "6. Divide the result in Step 5 by 5  **I get 39**\r\n" );
document.write( "7. Subtract 9 from the result in Step 6  **I get 30**\r\n" );
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document.write( "I notice that 30 is 3 times the 10 that I started with.\r\n" );
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document.write( "See what happens with 7\r\n" );
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document.write( "1. Think of a number. **I chose 7 pls**\r\n" );
document.write( "2. Multiply the number by 5.  **I get 35**\r\n" );
document.write( "3. Add 17 to the result in Step 2.  **I get 52**\r\n" );
document.write( "4. Triple the result in Step 3.     **I get 156**\r\n" );
document.write( "5. Reduce the result in Step 4 by 6  **I get 150**\r\n" );
document.write( "6. Divide the result in Step 5 by 5  **I get 30**\r\n" );
document.write( "7. Subtract 9 from the result in Step 6  **I get 21**\r\n" );
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document.write( "Wow, 21 is 3 times 7, the number I started with.\r\n" );
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document.write( "So all three times I got 3 times what I started with.\r\n" );
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document.write( "So my conjecture is: You always get 3 times the number you choose.\r\n" );
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document.write( "So this time I'll choose a variable, which can stand for ANY number\r\n" );
document.write( "and see what happens.\r\n" );
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document.write( "See what happens with variable N\r\n" );
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document.write( "1. Think of a number.\r\n" );
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document.write( "I choose \r\n" );
document.write( "N\r\n" );
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document.write( "2. Multiply the number by 5\r\n" );
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document.write( "I get \r\n" );
document.write( "5N\r\n" );
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document.write( "3. Add 17 to the result in Step 2.\r\n" );
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document.write( "I get \r\n" );
document.write( "5N + 17\r\n" );
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document.write( "4. Triple the result in Step 3.\r\n" );
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document.write( "I get \r\n" );
document.write( "3(5N + 17)\r\n" );
document.write( "Simplify\r\n" );
document.write( "15N + 51\r\n" );
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document.write( "5. Reduce the result in Step 4 by 6\r\n" );
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document.write( "I get\r\n" );
document.write( "15N + 51 - 6\r\n" );
document.write( "Simplify\r\n" );
document.write( "15N + 45\r\n" );
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document.write( "6. Divide the result in Step 5 by 5\r\n" );
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document.write( "I get:\r\n" );
document.write( "\"%2815N+%2B+45%29%2F5\"\r\n" );
document.write( "Simplify\r\n" );
document.write( "\"15N%2F5+%2B+45%2F5\"\r\n" );
document.write( "\"3N+%2B+9\"\r\n" );
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document.write( "7. Subtract 9 from the result in Step 6.\r\n" );
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document.write( "I get:\r\n" );
document.write( "3N + 9 - 9\r\n" );
document.write( "Simplify\r\n" );
document.write( "3N\r\n" );
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document.write( "3N is 3 times N, the number I started with.\r\n" );
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document.write( "So now my conjecture is proved because N can be ANY number!\r\n" );
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document.write( "The proved conjecture is: You always get 3 times the number you choose.\r\n" );
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document.write( "Edwin

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