Question

Solve the following inequality and write your answer using interval notation.
(x+4/10)≤(2/11-3x)

Answer 1

(x+4)/10 - 2/(11-3x) <= 0
multiplu yhtu by 10(11-3x)
(x+4)(11-3x) - 20 <= 0
11 - 3x^2 + 44 -12x - 20 >= 0
3x^2 + x -24 <= 0
(3x-8)(x+3) <= 0
critical points are 8/3 and -3
graph U shaped

solution is x <= -3 , x >= 8/3

Answer 2

oh you need interval notation
x = (-infinity,-3] and [8/3, +infinity)

Answer 3

theres a typo on 4th line - 11x not 11

Answer 4

Jimmy, I am having following your 4th line
11-3x^2+44-12x-20 how does this become 3x^2 +x-24?

Answer 5

11x and also another typo <= not >= - sorry

Answer 6

I see

Answer 7

i did it ok on paper but made typos when copying
i think its correct bu ill check it out on wolfram alpha

Answer 8

I got down to
-3x^2-x+44<=0
3x^2 +x _44>=0
and got confused!

Answer 9

What did Wolfram alpha say?

Answer 10

what happened to the rest of the post??????

Answer 11

I see that Wolfram Alpha got 11/3 on the positive side.

Answer 12

the correct solution according to wolfram is
x <= -3 as i got or (-infinity,-3]
and also
[8/3, 11/3)

i somehow missed another critical point in my solution.

Answer 13

(x+4)(3x-11)>=0
As you can see I messed up somewhere.

Answer 14

http://www.wolframalpha.com/input/?i=%28x%2B4%29%2F10+-+2%2F%2811-3x%29+%3C%3D+0

Answer 15

There is a difference between -4 and -8/3 !!lol

Answer 16

Hey between us, we got the right points. lol

Answer 17

mandaboo, please be tolerant lol

Answer 18

@jimmy: the problem is in your early step when you multiplied through by 11-3x

We have to consider the two cases where this is positive and where it is negative.

Answer 19

http://www.wolframalpha.com/input/?i=%28x%2B4%29%2F10+%E2%89%A4+2%2F%2811-3x%29

Answer 20

aahh - of course ! - thanx james