Observe that

    <— because 

  <— because 



—

Starting with this:

     a < c     (  )



we can use the property of inequalities:  if  a < c, then a - b < c - b to write:



        (1)



Now, if  a=b  and c>d then  a-c < b-d, so we can also write:

          (2)

because 

--

Combining (1) and (2):

     





—



Finally, by using  a < b < c  —>  a < c, and applying it to the inequality above:



       





[ 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.  ]   



       

RELATED QUESTIONS

PLEASE PLEASE PLEASE PLEASE PLEASE HELP ME. 

√(2)[√(4y) - √(18)]... (answered by stanbon)

 Multiply:

(5√[2] + 3)(√[2] – 2√[3])
 (answered by stanbon,MathLover1)

Multiply:
(5√[2] + 3)(√[2] – 2√[3])
 (answered by Fombitz)

√(X-2)=... (answered by funmath)

.  Multiply:
(5√[3] + √[5])(√[3] – 2√[5])
 (answered by adamchapman)

  Multiply:
(5√[3] + √[5])(√[3] – 2√[5])
 (answered by jim_thompson5910)

Multiply:
(5√[3] + √[5])(√[3] – 2√[5])
 (answered by jim_thompson5910)

Multiply:
(√[3] + 2√[5])(6√[3] – √[5])

?????    
	            (answered by jim_thompson5910)

i am asked to multiply


(√[3] + 4√[5])(2√[3] –... (answered by checkley77)

 Multiply:

(5√[2] + 3)(√[2] - 2√[3])

Please show howyou get the... (answered by sdmmadam@yahoo.com)