+0

0
738
2
+88

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

Apr 15, 2015

#2
+95179
+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 :) Apr 16, 2015 2+0 Answers #1 +94526 +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 Apr 15, 2015 #2 +95179 +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    $$(-\infty,-3)\;\;and\;\;(0.5,2)$$