Absolute Value Equations

Hey guys, this is A.J. I totally forgot to blog yesterday so I'm very sorry. I also forgot how to make a new post so I was staring at the page for like 2 minutes. ANYWAY. Let's go a head and explain this. *cough* vote for me


As you learned 2 days anything number in the absolute value brackets will be positive. so |3|=3 and |-3|=3.
With absolute value equations is the same thing.
Let's start with something easy like
|x|=3

so
x=3
or
-|x|=3
-x=3
x=-3

now we check
|3|=3
3=3

|-3|=3
-(-3)=3
3=3
WOW!lulz they both match up so they are both correct
get it? well hopefully you do. well I'm done. Just kidding.

Let's step it up now.
|x-3|=2
positive
(x-3)=2
take 3 to the other side
x=2+3
x=5
negative
-(x-3)=2
distribute the negative
-x+3=2
move 3 to the other side
-x=2-3
-x=-1
multiply both sides by -1 to make them x positive
x=1

Now let's check
|(5)-3|=2
5-3=2
2=2 wow check it, it works
let's check the other one
|(1)-3|=2
|1-3|=2
|-2|=2
since the -2 is in the absolute value brackets it will equal 2
thus
2=2
WOAH! that works as well. now you can vote for me

Now let's go super hardcore.
7+|1-3n|=33
positive
7+(1-3n)=33
7+1-3n=33
8-3n=33
take 8 to the other side
-3n=33-8
divide both sides by -3
-3n=25
-3=-3

n=25
***3
Now negative
-(7-|1+3n|)=33
7-1+3n=33
6+3n=33
take 6 to the other side
3n=33-6
3n=27
­­­­­­*3=3
n=9

now check it
7+|1-3(25)|=33
*******-3*****
-3 ● 25 = -75
1 ● -3 = -3

8 ● 75
****-3**
8 ● 3 = 24

|24-75|=51
|-51|=51
wow it's good next part
7+|1-3(9)|=33
8-27=33
-19=33
-19 does not equal to 33
so that part doesn't work so
x=25
**-3

wow. that was just really tiring so yeah just going to bling this out so people will vote for me and like spam it with cute things (:








kay yeah vote for me for like kay alright