SOLUTION: -5 < 2(2-s) + 1 &#8804; 9

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Question 793359: -5 < 2(2-s) + 1 ≤ 9
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
(1) -5%3C2%2A%282-s%29%2B1%3C=9
This is a "two sided" inequality which will give an interval space for the possible values of the variable, s in this case. The solution is straight forward - you solve each "side" separately as follows.
First solve the left side inequality given by
(2)-5%3C2%2A%282-s%29%2B1 or
(3)-5%3C2%2A2-2%2As%2B1 or
(4)-5%3C4-2%2As%2B1 or
(5)-5%3C5-2%2As or
(6)2%2As%3C5%2B5 or
(7)2%2As%3C10 or
(8)s%3C5
Now solve the right half of the inequality
(9)2%2A%282-s%29%2B1%3C=9
(10)4-2%2As%2B1%3C=9
(11)5-2%2As%3C=9
(12)-2%2As%3C=4
(13)-4%3C=2%2As
(14)-2%3C=s
Our two sided answer is given by (14) and (8) as
(15)-2%3C=s%3C5
If you put the limits of (15) into (1) you should get the two sided limits of (1).
When s = -2 in (1) we get
(16)-5%3C2%2A%282%2B2%29%2B1%3C=9 or
(17)-5%3C8%2B1%3C=9
(18)-5%3C9%3C=9
When s = 5 in (1) we get
(19)-5%3C2%2A%282-5%29%2B1%3C=9 or
(20)-5%3C-6%2B1%3C=9 or
(21)-5%3C-5%3C=9
Answer: -2%3C=s%3C5