Absolute Value Equations Help!

[sofidoremi]

How do you solve |2x+6|=8? Today our teacher gave us some notes about case 1 and case 2 to solve this but I don't understand how he did the question. This is an example:

Case 1: |2x+6|=8
x<(-3)
-(2x+6)=8
x=(-7)
so where why is x<-3? where did the -3 come from?

case 2:
x is less than or equal to -3
2x+6=8
x=1

x=-7, 1

I don't understand how this is done or why you do what you do for this. Can you please explain and walk me through the steps so I can understand it?
Thanks!

 

[wjm11]

How do you solve |2x+6|=8?

I don’t understand the notes you got from your teacher, but we don’t need them.

This is not complicated. It’s actually very simple: We will remove the absolute value signs and write two separate equations – one positive and one negative:

Positive (just drop the abs value):
|2x+6|=8
2x + 6 = 8
2x = 2
x =1

Negative (drop the abs value, but put a “-“ out front):
|2x+6|=8
-(2x+6)=8
-2x –6 = 8
-2x = 14
x = -7

That’s it! Easy, huh?