SOLUTION: 6|7+7n|+8<50

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Question 1107360: 6|7+7n|+8<50
Answer by ikleyn(52781) About Me  (Show Source):
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6|7 + 7n| + 8 < 50  ====>

6|7 + 7n| < 50 - 8

6|7 + 7n| < 42      ====>  divide both sides by 6  ====>

 |7 + 7n| < 7       ====>  divide both sides by 7  ====>

 |1 + n|  < 1       ====>  same as                 ====>

 |n + 1| < 1        ====>   same as  |n - (-1)| < 1.


The solution to the last inequality is the set of real numbers n that are remoted LESS THAN 1 unit from the number 

(from the point in the number line) "-1",  i.e.  -2 < n < 0.


Answer.  The solution is the set  -2 < n < 0,  or, in the interval notation,  the interval  (-2,0).