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

1 Answer
Aug 29, 2015

Answer:

#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)#.