Question 315116: The depth d of an aquarium tank for dolphins satisfies |d-50|<5,
Rewrite this a compound inequality that does not involve the absolute value function.
Answer by malaydassharma(59)   (Show Source):
You can put this solution on YOUR website! When (d-50) is positive, then (d-50) < 5 .......(i)
When (d-50) is negative, then it can be written as (50-d) < 5
or (d-50) > -5 .... multiplying both side by -1.
or -5 < (d-50) ................(ii)
Combining (i) and (ii) , we get
-5 < (d-50) > 5
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In another way,
|d-50|< 5
means , when d>=50 , (d-50) < 5 or d < 55
and , when d<=50 , (50-d) < 5 or d > 45
So, 45 < d < 55
or (45-50) < (d-50) < (55-50)
or -5 <(d-50)< 5
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