Re: Solution of (2x-1)(x+3)<=9

Quadratic inequality



(2x-1) (x+3) <=9

2x^2 + 5x -3 <= 9

2x^2 + 5x -12 <= 0

(2x - 3) (x + 4) <= 0

Product =0 then one factor = 0                             Product <0 then

one factor <0

2x - 3 = 0 OR x + 4 =0        OR     2x - 3 < 0 AND x+ 4 > 0      OR 
    2x - 3 > 0 AND x + 4<0

2x = 3                                             2x < 3 
2x > 3

X = 3/2 OR x = -4               OR             x < 3/2 AND x > -4 
OR           x > 3/2 AND x < -4

<--(-4)------------(3/2)---->  OR   < --(-4)///////////////////(3/2)----> 
OR   //////(-4)------------(3/2)////////

                                                                          
  
                                           { } empty set

<-----(////)/////////////////////////////////(////)-------à 
No way can x be both <-4 AND >3/2

           -4                                               3/2

"Jim" <MyrskyVaris@[EMAIL PROTECTED]
> wrote in message 
news:d29292fc-d848-42c1-b055-6fb1402c7846@[EMAIL PROTECTED]
> Hello
>
> Please help me with the correct approach to the solution for (2x-1)(x
> +3)<=9 .
>
> We get multiple choice answers, like 1) x <= -4 or x >= 3/2  or 2) -4
> <= x <= 3/2
>
> What approach do I use?
>
> What is this type of question called?
>
> Thank you.
>
> Jim