SOLUTION: I don't understand inequalities. how does one translate this into simple English.
-2x≤g(x)≤2x
Thanks
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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 ]
-------------------------------------------
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 ]
--------------------------------------------------
You have to keep in mind that is a true statement
The quantities can be any number on the number line
--------------------
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
---------------------
As for your example, it reads:
The function is LESS THAN OR EQUAL to
and is also GREATER THAN OR EQUAL to
------------------------------------------------
You don't have to put this on one line
You can break it up into 2 statements:
-----------------
Also note that you can spin the inequality around and
it's still true:
is perfectly valid also
------------------
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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