Solve the inequality and write your answer in interval notation.

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 :)

(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