document.write( "Question 1094630: Using the properties of equality prove that 5√2 - √11 < 5√3 - 3 \n" ); document.write( "

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Using the properties of equality prove that 5√2 - √11 < 5√3 - 3
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\n" ); document.write( "EDITED TO: Using the properties of inequalities prove that 5√2 - √11 < 5√3 - 3
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document.write( "Observe that
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document.write( "  <Ч because \r
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document.write( "Starting with this:
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document.write( "     a < c     (  )\r
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document.write( "we can use the property of inequalities:  if  a < c, then a - b < c - b to write:\r
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document.write( "        (1)\r
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document.write( "Now, if  a=b  and c>d then  a-c < b-d, so we can also write:
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document.write( "          (2)
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document.write( "because 
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document.write( "Combining (1) and (2):
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document.write( "     \r
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document.write( "Finally, by using  a < b < c  Ч>  a < c, and applying it to the inequality above:\r
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document.write( "       \r
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document.write( "[ In words, you are starting with a value less than another (a < c), and then subtracting values from each of 'a' and 'c'.   The value subtracted from 'a' is greater than the value subtracted from 'c' which makes a-b even smaller than c-d.  ]   \r
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