# 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