How do you solve x^2+16x+24>6x?

2 Answers
May 25, 2018

x<-6or x>-4

Explanation:

simplifying to x^2+10x+24>0

solving x^2+10x+24=0 we get
x_1=-4
x_2=-6
so our inequality is equivalent to
(x+4)(x+6)>0
this gives us
x>-4 or x<-6

Aug 9, 2018

x in (-oo, -6) uu (-4, oo)

Explanation:

Given:

x^2+16x+24 > 6x

Subtract 6x from both sides to get:

x^2+10x+24 > 0

We can make the left hand side into a perfect square trinomial by adding 1, so let us add 1 to both sides to get:

(x+5)^2 = x^2+10x+25 > 1

Note that this would give equality when (x+5)^2 = 1, i.e. when x+5 = +-1, i.e. when x=-6 or x=-4.

Hence the inequality is achieved when:

x < -6" " or " "x > -4

In interval notation, when:

x in (-oo, -6) uu (-4, oo)