Question

How do you solve the inequality: `(x+6)(x-6)>0`?

Answer 1

`x in (-oo, -6) uu (6, + oo)`

Explanation:

Notice that the left-hand side of the equation is actually a product of two expressions, `(x+6)` and `(x-6)`.

In order for this product to be positive, you need both terms to either be positive or either be negative.

For values of `x > 6` you get that

`{(x+6 > 0), (x-6 >0) :} implies (x+6)(x-6) > 0`

For values of `x < -6` you get that

`{(x+6 < 0), (x-6 < 0) :} implies (x+6)(x-6) > 0`

This means that any value of `x` that is smaller than `(-6)` and any value of `x` that is greater than `6` will satisfy this inequality. The solution set will thus be `x in (-oo, -6) uu (6, + oo)`.