How do you solve #\frac { 1} { 2} x ^ { 2} - x > 4#?
1 Answer
or
Explanation:
Bring everything to one side.
#1/2 x^2 - x - 4 > 0#
Factor that side if possible.
Factor the
#1/2 (x^2 - 2x - 8) > 0#
Recognize that
#1/2(x-4)(x+2)>0#
Divide both sides by
#(x-4)(x+2)>0#
We now have a product of two factors on the left:
Both factors depend on
The 1st factor,
The 2nd factor,
So both factors will be negative when
Similarly, both factors will be positive when
Our solution is all