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What is the sum of all integers $n$ that satisfy
$$-3n < 7n-20 < 3n~?$$

$($In other words, what is the sum of all integers $n$ that satisfy both of the inequalities
$$-3n<7n-20\text{~~and~~}7n-20<3n~?)$$

 May 10, 2015

Best Answer 

 #1
avatar+33616 
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-3n < 7n - 20                        7n - 20 < 3n

0 < 10n - 20                          4n - 20 < 0

20 < 10n                                4n < 20

2 < n                                       n < 5

 

So n is greater than 2 and less than 5. That is, n can only be 3 or 4. The sum of 3 and 4 is 7

.

 May 10, 2015
 #1
avatar+33616 
+10
Best Answer

-3n < 7n - 20                        7n - 20 < 3n

0 < 10n - 20                          4n - 20 < 0

20 < 10n                                4n < 20

2 < n                                       n < 5

 

So n is greater than 2 and less than 5. That is, n can only be 3 or 4. The sum of 3 and 4 is 7

.

Alan May 10, 2015

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