How do you solve #x^2+16x+24>6x# using a sign chart?

1 Answer
Dec 29, 2016

x<-6 or x>-4


Simplify the quadratic inequality as shown and factorise it as (x+6)(x+4)>0. Now divide the entire numberline in three intervals #(-oo,-6), (-6,-4) and (-4,oo)#.

In each interval select a test value and determine the sign of (x+6), (x+4) and then sign of (x+6)(x+4). The intervals in which the sign of (x+6)(x+4) is +ive indicate that Inequality holds good in those intervals. The value of x in these intervals is the required answer. In the present case Inequality holds good in intervals#(-oo,-6) and (-4,oo)#. This means x<-6 or x>-4 is the required solution.
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