Please help.
I'm having a lot of trouble with solving inequalities and graphing them
solve the inequality and graph the solution on the real number line
x^2+x-6/x
I got SS: -infinity to -3 including -3 union -2 to infinity including -2
is that right?
EDIT WHERE INEQUALITY IS GREATER THAN OR EQUAL TO ZERO
do you mean
6/x
or do you mean
(x^2+x-6)/x
????
Sorry i should have put that in parenthesis
(x^2+x-6)/x greater than or equal to 0
well we know that when x = 0, it is -6/0
which is undefined but is huge positive for x small negative and huge negative for x small positive, so sketch that on your graph.
for x large positive x + 1 - (6/x) looks like y = x so draw a line sloping up at 45 degrees for large positive x
for x large negative x + 1 -(6/x) looks like y = x again so sloping down at 45 degrees in quadrant 3
Now, where is it zero?
x^2 + x - 6 = 0
(x-3)(x+2) = 0
x = -2 or x + +3
well, that does it, look at your graph sketch
it is positive from x = -2 to x = 0
it is positive from x = 3 to x = +oo
(x+3)(x-2) = 0
x = -3 or x = +3
positive from x = -3 to x = 0
positive from x = +2 to x = +oo
Isn't it x^2+x-6 = 0
(x+3)(x-2) = 0?
x = -3 or x= +2?
x = 3 or x = +2 I mean
x = -3 or x = +2
I ended up with SS: (-00,-3]union [2,00)
why would it be -3 to 0?
because it is zero at -3
then when x approaches zero from the left it is like -6/-.00000001 which is big positive