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(x + 3)(2x - 1)(2 - x) > 0

zandaleebailey  Apr 15, 2015

Best Answer 

 #2
avatar+91045 
+10

I would consider the graph

y=(x+3)(2x-1)(2-x)    

The roots are  -3, 1/2, and 2

 

It is of the form    

 

 $$\\y=-ax^3+bx^2+cx+d\\\\
$Where a,b,c and d are real numbers and a is positive.$$$

 

****    I instantly know the shape of this graph.    ****

 

Refer to this post that I did in the past to understand what I mean.

It will help you enormously if you understand this older post  !!!

http://web2.0calc.com/questions/how-do-you-find-a-power-function-that-is-graphed

 

Here is the graph.  I have hidden the y axis because it is not relevant.

you do not need a graphing calc to get this basic shape.  It is easy to draw freehand.

The answer is all the x values where the graph is ABOVE the x axis.  It is that easy!

You do not need to test any points!

 

Solutions    $$(-\infty,-3)\;\;and\;\;(0.5,2)$$

 

If you have any questions please ask.    

If you fully understand this you will be a step in front of many others :)

Melody  Apr 16, 2015
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2+0 Answers

 #1
avatar+78741 
+10

(x + 3)(2x - 1)(2 - x) > 0

Setting each factor to 0, we have the following possible solution intervals....

(-∞, -3), (-3, 1/2), (1/2, 2), (2, ∞ )

We can pick a point in each interval to see if that interval satisfies the inequality

Picking -5 in the first interval will make the inequality true

This lets us know that the other interval that will "work" occurs on (1/2, 2)

Then, the solutions come from (-∞, -3) and (1/2, 2)

See the graph here.....https://www.desmos.com/calculator/1l4dwzcpor

 

  

CPhill  Apr 15, 2015
 #2
avatar+91045 
+10
Best Answer

I would consider the graph

y=(x+3)(2x-1)(2-x)    

The roots are  -3, 1/2, and 2

 

It is of the form    

 

 $$\\y=-ax^3+bx^2+cx+d\\\\
$Where a,b,c and d are real numbers and a is positive.$$$

 

****    I instantly know the shape of this graph.    ****

 

Refer to this post that I did in the past to understand what I mean.

It will help you enormously if you understand this older post  !!!

http://web2.0calc.com/questions/how-do-you-find-a-power-function-that-is-graphed

 

Here is the graph.  I have hidden the y axis because it is not relevant.

you do not need a graphing calc to get this basic shape.  It is easy to draw freehand.

The answer is all the x values where the graph is ABOVE the x axis.  It is that easy!

You do not need to test any points!

 

Solutions    $$(-\infty,-3)\;\;and\;\;(0.5,2)$$

 

If you have any questions please ask.    

If you fully understand this you will be a step in front of many others :)

Melody  Apr 16, 2015

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