Question

x^2+x+7>19 (Solve for x)

Answer 1

factor
\[x^2+x-12>0\]
\[(x+4)(x-3)>0\]

Answer 2

now this animal is a parabola that faces up . it is zero at -4 and 3 so you can tell from the picture (in your head) that it is positive from
\[(-\infty,-4)\] and on
\[(3,\infty)\]

Answer 3

with the understanding that "positive" is a synonym for "above the x axis"

Answer 4

we can start it by subtracting 19 from both sides

Answer 5

x^2+x+7-19>19-19

x^2 +x -12 > 0 ; now its just a quadratic to factor

Answer 6

what 2 numbers multiply to get 12?

Answer 7

1*12
2*6
3*4

so we got to see which set gets us a value for the middle# of +1

12 __ 1 = 1 will a + or - make this happen? no

6 ___ 2 = 1 can a + or - make this happen? no

4 __ 3 = 1 ; this is a good bet; use 4-3

(x+4)(x-3)

Answer 8

now we determine what = 0

x+4 = 0 when x=?

x-3 = 0 when x=?

and use those value on our number line

Answer 9

i hate this method!

Answer 10

<.....-4.......3......>
_ + + ; for (x+4)
_ _ + ; for (x-3)
------------------
+ - + ; multiplied together we get the results

Answer 11

so our answers is as sat gave:

(-inf,-4) U (3,inf)

Answer 12

although i do like our explanation

Answer 13

:)

Answer 14

"your" explanation i meant

Answer 15

graph please? to make sure i did it right :)

Answer 16

anybody?