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that is ok I'm keeping on, thank you
I'll show you what I did,,,
when (x-9) (x-1) ≥ 0
(x-9) = 0 , x=9 the interval is [9,∞) , test a value between this interval : "10" : 10^2 - 10*10 +9 ≥ 0 , +9 ≥ 0 and that is true!
(x-1) ≥ 0 x=1 the interval is [1,∞) , test a value between this interval : "2" : 2^2 - 10*2 +9 ≥ 0 , -7 ≥ 0 , and that is WRONG! so Switch this inequality and become : x ≤ 1 , the interval is : (-∞,1]
sol : (-∞,1] U [9,∞), except -3
is that ok? hehehe
I think I got is thanks for your help
I mean how do you solve this ? what is the steps do it here please
sure,,, but what is the right answer now?
but how that can be? x<= 1??
if we put -3 in it will be |-3+3| , zero,, and that is wrong right?
how did you do that
I finish the first link math isfun.com
is the sol : : [9,∞] ∩ [1,∞)
not U?
and if yes why ∩????
is cause will be either the first interval or the second one??
please I need answers I get board from trying I have a lot of topics in maths to finish
I was study factoring and Quadratic Equations but I just started to study (Solving Quadratic Inequalities),
and I stuck with the first example,, I'll finish it...
I think yes, maybe
x-9 ≥ 0 =>>>>>>>>> x≥9 then [9,∞)
and x-1≥0 =>>>> x≥1 then [1,∞)
sol : [9,∞] U [1,∞)
is that right?? but the answer of my teacher is different???,
by the way thank you for this link I study the factors and quadratic equations,
yes and what is the next
I mean I stuck in this point,,, what I have to do now? please I want full solution I really have an exam after one week in such topics..
hello
I tried to solve these two question about absolute value inequality but I stuck with x^2 and with number 2
please see this picture and solve this two for me, the answer of my teacher for 1) is (-∞,1] U [9,∞)
and for 2) is (-∞,∞)
is it right?
I tried the a way that a member learned me that here but I stuck
solve this in short way for me please!!! it takes me 3 days and I didn't find any solution :
can't be a solution, because while
and what is that mean if I mean from where did you get |-1+3| there is just |x-3| and |x+1| in the expression I don't see |x+3|?
and do you mean it can't be equal to -1 because when we replace -1 by |x-3| ≤ |x+1| it will be |-1-3| ≤ |-1+1| then |-4| ≤ |0| and that is false it can't be -1, ... is that right? is I'm doing a good step or not....
So now you know that the values for which your inequality hold are:
and
The intersection of these sets is . That is, the result of combining the above two inequalities isTo summarise, the left-hand side of what your lecturer wrote is fine. For the rest, see the above.
you said inequality are hold x > -1
and x ≥ 1.
so where is number zero? why the inequality sol is not [0,∞) ?
Sometimes it is more intuitive to explain it in the alternate form, which is also applicable for absolute values.
And yes, heed zetafunc's warning, sometimes it can introduce extraneous solutions.
may you please solve it like my lecturer did but in simple way without these strange number lines and +++ or ---
if you have a free time please, I need you sol with your elegant words and short steps. with greater and smaller and with interval notations.
The important part to take away from your lecturer's solution is that is equivalent to
but mathegocart didn't do like the lecturer did, what does it changed? how the solution is
,and the sol of the teacher is :
, U {-1}.it's important in general to go back and check whether or not the solutions you've found are actually valid.
but how to do that? I mean how to check wether or not the solution is valid or not????
how did you know the solution was fine please help with that...
Believe me if there is another way to help myself with, I'm sure I'll follow this way, but this is the only place that I can get help with a specific questions in math.
thank you very much.
so....is this the end of the solution? but how did you do that with an absolute value? ((( I mean we must take two possibilities once in >=0 and once in < 0 )))))???
please see this following picture, is the the solution of our lecturer in the university :- what is this? I really hop you to help me with full details about that
I always asking him about problems but our lecturer don't show respect to who ask him about that he learning us he just writing these problems without careful and caring ...
thank you for this great example,
can I ask you another question it was difficult to me to solve it :-
<=or like this
<= 1please may I get the full solution for this? with its interval notation
thanks,,, and maybe I need to put a root inside this fraction
what can I write
how to write the number line? and how to write the numerator and denominator fractional and how to put a variables inside the absolute value? I mean inside bars | | | | ?
thank you bobbym,
and #zetafunc sorry but I don't understand these symbols you provided, I'm not like you I just do simple mathematics I don't even know what is
#Mathegocart
yes thank you very much I got it now.
but can we say the abs -6 is -6 too? cause it is just a sign. what will happen if we say that
Hello, .... I'm zaid and nice to meet you all
I just feel that I'm very annoying here and don't make people feel happy
because I ask too much then usual ( that because of my bad past in mathematics). so if anyone feel that I'm disturbed just tell me and I'll leave the forums.
or if anyone from this point that have an advice for me, please go ahead and tell me.
Greeting
Hi,
I study the absolute value maybe more than 2 times in my life,, when I was in the school and now and on the internet for myself
now I read (Absolute Value how far a number is from zero) .. then it is mean abs for 6 is 6 and -6 is 6
what is the meaning of that? and if it was about how far the number 6 from zero is the meaning of abs
then why -6 is 6 ? why the abs -6 is -6?
I apologize for such questions again and again.. I don't have another way to understand! sorry
thank you very much ...