inequalities /:
- Thread starter hailee
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JeffM
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hailee said:im having trouble with this problem
6<x+4?11
You do not really say what you are supposed to do with that relationship. I am guessing, however, that you are supposed to simplify it.
WITH RESPECT TO addition and subtraction, the rules of manipulation are the same for inequations as for equations. You can add equals to each expression or subtract equals from each expression.
So
6 < (x + 4) \(\displaystyle \leq\\) 11
So (6 - 4) < (x + 4 - 4) \(\displaystyle \leq\\) (11 - 4)
So 2 < x \(\displaystyle \leq\\) 7.
The rules are a bit more complex when it comes to multiplication and division.
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FluifePele
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Nataly Portman
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Deleted member 4993
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tonyromo said:
-6 >= x+7 >= 6
Now follow the example worked out above....
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JeffM
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Hi Tonytonyromo said:
This is your first post. A few tips.
(1) Use the NEWTOPIC button to post a brand new question. People will assume, if you add to an old thread, that the question has been answered and so may inadvertently ignore you.
(2) Explain just exactly where you are stuck, show your work to date, and explain where you are in your math studies. An answer that is good for a calculus student will not help someone just starting algebra. If we do not know what you have tried and what you already know, we do not know where to start helping.
(3) Make the question you are asking as clear as possible. We cannot see your text book. I cannot be certain what your teacher wants you to do with that inequality above.
(4) Read the thread entitled "Read Before Posting."
I am going to assume that your teacher wants you to simplify the inequality above into something in terms of x alone or maybe |x| alone, but I am guessing because you have not given a question.
A fundamental rule about absolute values is this:
if (y * z) >= 0, |y + z| = |[|y| + |z|]|, BUT
if (y * z) < 0, |y + z| = |[|y| - |z|]|.
Now in the expression |x + 7|, 7 > 0. But x may be positive or negative. So you should be thinking along two main tracks, one for non-negative x and one for negative x. Let's FIRST try the non-negative path |x + 7| > 6. What non-negative values of x make that statement true? I know this is an easy question, but I am showing you a method that you can use for more complex problems.
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