Home > Algebra > Absolute Value Equations

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

Answer 1

Ethan Adkins

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

The definition of an absolute value is:

#|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#

As a result, we must resolve both:

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

#3x+6>15#

#3x>9#

#x>3#

#-(3x+6)>15#

#3x+6<-15#

#3x<-21#

#x<-7#

This provides us with:

#-oo < x< -7#

and

#3 < x < oo#

This can be stated as the union of intervals:

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

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Genesis Allen

To solve the inequality |3x + 6| > 15, you first isolate the absolute value expression. Then, you split the inequality into two cases: when the expression inside the absolute value is positive and when it's negative. Finally, solve for x in each case.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #|3x + 6| &gt;15#?

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