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09 Jul 2020, 05:06
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Hello guys!
I have been solving inequalities problem in forum and have observed that some of the members are not aware about the wavy curve method to solve an inequality.
I'll try to explain this method with the help of an example.
Firstly, I'll list down the step to solve this inequality by wavy curve method:-
Step 1 :- Make the right side of inequality zero and covert the equation in linear factors [e.g. if you have \((x^2)-1\), then you may write it as (x+1)(x-1)]
Step 2 :- Coefficient of x must be positive in all the factors, if that is not the case then make it positive using the appropriate mathematical operation [e.g. (1-x)(x-7)>0 should be transformed and written as (x-1)(x-7)>0]
Step 3 :- Now put all the factors equal to zero and put these values on the number line
Step 4 :- Put "+" sign on the extreme right side and change the sign alternatively
Step 5 :- Now select the region as per the condition given in the question statement. Inequality will be positive for "+" regions and negative for "-" regions.
Let us say we have an inequality to be solved ->
(x-1)(x+2)(3x-5)<0 and question asks to solve for x
Solve each factor individually and put the corresponding values on number line and start marking the regions from extreme right side and then alternatively change the sign.
Points to be market on number line are :-
1 -> by putting x-1=0
-2 -> by putting x+2=0
5/3 -> by putting 3x-5=0
Mark these points on the number line as shown in picture.
Inequality Pic.png [ 123.31 KiB | Viewed 3694 times ]
Now, we need the region where inequality is less than zero, so we will consider all the area with "-" OR negative sign to be our answer
Thus, x belongs to (-infinity, -2) U (1,5/3)
I have been solving inequalities problem in forum and have observed that some of the members are not aware about the wavy curve method to solve an inequality.
I'll try to explain this method with the help of an example.
Firstly, I'll list down the step to solve this inequality by wavy curve method:-
Step 1 :- Make the right side of inequality zero and covert the equation in linear factors [e.g. if you have \((x^2)-1\), then you may write it as (x+1)(x-1)]
Step 2 :- Coefficient of x must be positive in all the factors, if that is not the case then make it positive using the appropriate mathematical operation [e.g. (1-x)(x-7)>0 should be transformed and written as (x-1)(x-7)>0]
Step 3 :- Now put all the factors equal to zero and put these values on the number line
Step 4 :- Put "+" sign on the extreme right side and change the sign alternatively
Step 5 :- Now select the region as per the condition given in the question statement. Inequality will be positive for "+" regions and negative for "-" regions.
Let us say we have an inequality to be solved ->
(x-1)(x+2)(3x-5)<0 and question asks to solve for x
Solve each factor individually and put the corresponding values on number line and start marking the regions from extreme right side and then alternatively change the sign.
Points to be market on number line are :-
1 -> by putting x-1=0
-2 -> by putting x+2=0
5/3 -> by putting 3x-5=0
Mark these points on the number line as shown in picture.
Attachment:
Inequality Pic.png [ 123.31 KiB | Viewed 3694 times ]
Now, we need the region where inequality is less than zero, so we will consider all the area with "-" OR negative sign to be our answer
Thus, x belongs to (-infinity, -2) U (1,5/3)
06 Dec 2020, 16:06
Kudos
Bookmarks
Thanks for sharing, buddy. Wavy line method is very helpful.
If anyone wants to check out some more example questions: https://www.google.com/search?client=fi ... rve+method
If anyone wants to check out some more example questions: https://www.google.com/search?client=fi ... rve+method
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