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The Algebra, 9 classes, Section IX, INEQUALITY, § 48, General information
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Determination: Number a is considered more b if difference a-b number positive; number a less b if difference a-b number negative
 
Problem 11. Compare importance of the function , if and .
Date:   01-09-2004
Decision:
   
y = 400     y = 400     400 - 400 = 0
400 = 400
The Answer: under x = -20 і x = 20 importances of the function in = equal.
Date:   01-09-2004
 
Problem 15. Prove that under each importance n:
а) ; б) ; в) ;
Date:   01-09-2004
Decision: а)

- ( -1 ) > 0     All numbers in uneven degree 0
0
a = - not negative
b = -1 - negative
a - b < 0 , after all
+ 1 > 0 under all importances n
Date:   01-09-2004
Decision: б)

If n > 50 , that n - 5 - positive ( >0 ), as well as
If n = 5 , that n - 5 = 0 , so
If n < 50 , that n - 5 < 0 , but
Thence under all importances n
Date:   01-09-2004
Decision: в)
-2n + 1 0

If n > 1 , that n - 1 > 0 , and
If n = 1 , that n - 1 = 0 , and
If n < 1 , that n - 1 < 0 , but
Answer: - 2n + 1 0 under all importances n
Date:   01-09-2004
 
Problem 16. Select several importances variable h, which satisfy the inequality:
а) ; б) ; в) ;
Date:   01-09-2004
Decision: а)
2x + 3 < 0
2x < -3
x < -1,5
= -2
= -3
= -1000
Date:   01-09-2004
Decision: б)
3 - > 0
3 >      < 3
> |3|
= 1
= -1
= 0
Date:   01-09-2004
Decision: в)


= 0
= -3
= -100
Date:   01-09-2004
§48   §49   §50
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