Inequality and Interval notation (Help needed)

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RicanGurl

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Sep 30, 2007
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I just started learning about inequalities. Describing the solution set with inequality notation, interval notation and making a graph. And I did this problem and found it easy.

The problem :

x+ 2 > or equal to 5


Finding the solution by subtracting by 2 from both sides :

x+ 2 -2 > or equal to 5 -2


The answer in inequality notation : x > or equal to 3

The answer in interval notation : (3, and the sign that looks like an 8)

and I drew the graph.


I am having trouble with this next problem : -x+2 >or equal to 5

Working it out (I subtracted 2 from both sides) : -x+ 2 -2 > or equal to 5 - 2


Answer I got : x > or equal to 3

which you flip that to x < or equal to 3


The answer in the book says that it is : x < or equal to -3

And in interval notation it says that both the sign that looks like an (8 , and 3) are negative. I dont understand how they are getting negative.

Please help!


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-x+2 >= 5
-x >= 3
x <= -3

Giving you a domain of all real numbers x such that x <= -3; x has to be less than or equal to -3

-oo <= x <= -3

Therefor, x can be any number in the range of -infinity to -3, where x <= -3 so -3 is included in the interval as shown below:

(-oo .. -3]

John
 
I got all the way to -x>= 3


I want to know why they take the negative from the x and give it to the 3

because the final answer is x =< -3

Why? why are the signs flipped if : -x +2 -2 >= 5-2
I end with this -x >= 3
But the book and you end with this x=< -3

????
 
I see that if it says -x >= 3

that would mean since in reality 3 is greater then a negative number, the negative would have to be added , right?


But even with that thinking, why would this: >= =< change?
 
Good question... here's the proof:

If a >= b

then a - b >= 0

then -b >= -a

so -a <= -b must be true
 
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