Stuck on chapter polynomial and rational inequalities

[mario99]

Hi again bladeren,

I will present a new approach to solve inequalities. This maybe a better way to solve inequalities for beginners. I hope that it will remove some stress.

Imagine that, we have this inequality: [imath]\displaystyle x^2 - x - 20 \leq 0[/imath]

First step is to factor: [imath]\displaystyle (x + 4)(x - 5) \leq 0[/imath]

This will give you:

[imath]\displaystyle x \leq -4[/imath], [imath]\displaystyle \ \ \ x \leq 5[/imath]

Always Choose The Larger Number (Before Flipping). So we have [imath]\displaystyle x \leq 5 \ \ \ \ \ [/imath] (1)

Now flip the inequality: [imath]\displaystyle (x + 4)(x - 5) \geq 0 [/imath]

This will give you:

[imath]\displaystyle x \geq -4[/imath], [imath]\displaystyle \ \ \ x \geq 5[/imath]

Always Choose The Smaller Number (After Flipping). So we have [imath]\displaystyle x \geq -4 \ \ \ \ \ [/imath] (2)


Combine (1) and (2). Then the answer is [imath]\displaystyle -4 \leq x \leq 5[/imath]

 

[jonah2.0]

Beer drenched reaction follows.

After all those videos and tutorials, i still dont understand qauadratic inequalities. I dont understand how to get a answer with a number line. Can someone help me please

If you really watched all those videos and tutorials, you'd understand how to deal with quadratic inequalities already. Perhaps I overestimated your resourcefulness in locating the specific subject matter. Give it another go and start with interval notation of Algebra 2.

 

[jonah2.0]

For quadratic inequalities, see College Algebra at

 

[jonah2.0]

From Algebra 2 (I totally missed that one),

 

[bladeren]

Thanks for the many replies.

 

[bladeren]

I see that they use an alternative method that I personally prefer over "plugging in a test value in each interval", namely using the factored form to see that everywhere in, say, the middle interval here, the first factor will be negative and the second factor will be positive, so the product, the expression you are interested in, is negative.

Here is how I like to mark up the number line, showing the sign of each factor, then of the entire product:

View attachment 38458​

Can you see what I'm doing there? It matches what they say in the paragraph under the picture.

I think i understand this one. Thanks for your reply.

 

[Harry_the_cat]

Hi again bladeren,

I will present a new approach to solve inequalities. This maybe a better way to solve inequalities for beginners. I hope that it will remove some stress.

Imagine that, we have this inequality: [imath]\displaystyle x^2 - x - 20 \leq 0[/imath]

First step is to factor: [imath]\displaystyle (x + 4)(x - 5) \leq 0[/imath]

This will give you:

[imath]\displaystyle x \leq -4[/imath], [imath]\displaystyle \ \ \ x \leq 5[/imath]

Always Choose The Larger Number (Before Flipping). So we have [imath]\displaystyle x \leq 5 \ \ \ \ \ [/imath] (1)

Now flip the inequality: [imath]\displaystyle (x + 4)(x - 5) \geq 0 [/imath]

This will give you:

[imath]\displaystyle x \geq -4[/imath], [imath]\displaystyle \ \ \ x \geq 5[/imath]

Always Choose The Smaller Number (After Flipping). So we have [imath]\displaystyle x \geq -4 \ \ \ \ \ [/imath] (2)


Combine (1) and (2). Then the answer is [imath]\displaystyle -4 \leq x \leq 5[/imath]

As a teacher who likes her students to understand what they are doing, I really don't like this method. There seems to be no reason for doing what you are doing.

 

[bladeren]

This explanation i liked. He made it simple.

 

[bladeren]

There are three methods to solve quadratic inequalitie for x. In this video she explains the three methods;

In this link you find the explanation for the sign table method;

 

[bladeren]

I wish i could find those three methods in one (work)book