Question 1003018: I don't understand inequalities. how does one translate this into simple English.
-2x≤g(x)≤2x
Thanks
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! Starting simple, suppose you have 2 quantities,
 and  , then
(1)  means:
[ quantity  ] is GREATER than [ quantity  ]
(2)  means:
[ quantity ] is LESS than [ quantity ]
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Now if you add on the equals sign, you have:
(3)  means:
[ quantity ] is GREATER than OR EQUAL to [ quantity ]
(4)  means:
[ quantity ] is LESS than OR EQUAL to [ quantity ]
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You have to keep in mind that  is a true statement
The quantities can be any number on the number line
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A potential sticky point is the following:
If you divide both sides by a negative number, then the
inequality sign has to be reversed.
Example:
Divide both sides by 
 oh-oh, this is NOT TRUE, but if
I reverse the inequality sign,
 OK now
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As for your example, it reads:
The function  is LESS THAN OR EQUAL to 
and is also GREATER THAN OR EQUAL to 
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You don't have to put this on one line
You can break it up into 2 statements:
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Also note that you can spin the inequality around and
it's still true:
 is perfectly valid also
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You can treat inequalities just like equations by adding,
subtracting, multiplying, dividing both sides by the
same quantity EXCEPT the special case of dividing by
a negative number just noted.
Hope this helps
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