How do you solve |3x + 6| >15?

1 Answer
Mar 28, 2018

(-oo,-7)uu(3,oo)

Explanation:

The absolute value is defined as:

|a| = acolor(white)(888888) if and only if color(white)(88888)a>=0

|a| = -acolor(white)(.888) if and only if color(white)(888888)a<0

Because of this we need to solve both:

3x+6>15 and -(3x+6)>15

I

3x+6>15

3x>9

x>3

II

-(3x+6)>15

3x+6<-15

3x<-21

x<-7

This gives us:

-oo < x< -7

and

3 < x < oo

We can express this as a union of intervals:

(-oo,-7)uu(3,oo)