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24 Jul 2013, 06:58
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Bookmarks
Hi
When we take the inequality (x-3)*(x-6)>0, I understand that this eq is a parabola that passes through the X-axis at x=3 and x=6.
This also shows that the expression is positive between x>3 and x 0, then is there a way to arrive at 3 0, I don't know whether the solution is a<x<b or b<x<a.
is there a way to arrive at this?
When we take the inequality (x-3)*(x-6)>0, I understand that this eq is a parabola that passes through the X-axis at x=3 and x=6.
This also shows that the expression is positive between x>3 and x 0, then is there a way to arrive at 3 0, I don't know whether the solution is a<x<b or b<x<a.
is there a way to arrive at this?
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24 Jul 2013, 08:29
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gmatter0913
That's not correct. (x-3)*(x-6)>0 means that x<3 or x>6:
Attachment:
MSP13131f9ac318511bi708000038f28af4a7ie7i53.gif [ 7.11 KiB | Viewed 2121 times ]
Solving inequalities:
x2-4x-94661.html#p731476 (check this one first)
inequalities-trick-91482.html
everything-is-less-than-zero-108884.html?hilit=extreme#p868863
xy-plane-71492.html?hilit=solving%20quadratic#p841486
Hope it helps.
24 Jul 2013, 22:55
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Hi Bunuel
Thanks a lot for those links and your wonderful contribution.
I realized that I am struggling specifically with the below:
For example, let us take the equation (x-1)(x-4)=0
So, when I look at the expression (x-1)(x-4), I know that it is a parabola passing through x=1 and x=4.
But, I don't know whether this is V-shaped parabola or an inverted V-shaped parabola. Currently, the way I am doing this is to substitute a value between the roots (for eg. x=2 in the above case) and if it is negative, I know that the curve is a V-shaped parabola. Hence the curve is +ve outside the points x=1 and x=4 and is -ve between the roots.
So, for the inequality (x-1)(x-4)>0 the solution is 4<x<1 (where is the curve +ve)
So, for the inequality (x-1)(x-4)<0 the solution is 1<x<4 (where is the curve -ve)
If you see the above, the crucial thing is to identify whether the curve is V-shaped or inverted V-shaped?
Currently, I am doing it using substitution method, and I feel it is prone to errors. So, I want to know is there any other way apart from substituting values to find out the shape of the curve?
I am extremely sorry for the repeated questions, but I really need some handholding on this topic. Kindly help me on this.
Thanks a lot for those links and your wonderful contribution.
I realized that I am struggling specifically with the below:
For example, let us take the equation (x-1)(x-4)=0
So, when I look at the expression (x-1)(x-4), I know that it is a parabola passing through x=1 and x=4.
But, I don't know whether this is V-shaped parabola or an inverted V-shaped parabola. Currently, the way I am doing this is to substitute a value between the roots (for eg. x=2 in the above case) and if it is negative, I know that the curve is a V-shaped parabola. Hence the curve is +ve outside the points x=1 and x=4 and is -ve between the roots.
So, for the inequality (x-1)(x-4)>0 the solution is 4<x<1 (where is the curve +ve)
So, for the inequality (x-1)(x-4)<0 the solution is 1<x<4 (where is the curve -ve)
If you see the above, the crucial thing is to identify whether the curve is V-shaped or inverted V-shaped?
Currently, I am doing it using substitution method, and I feel it is prone to errors. So, I want to know is there any other way apart from substituting values to find out the shape of the curve?
I am extremely sorry for the repeated questions, but I really need some handholding on this topic. Kindly help me on this.
