Question

please help!;
2[x-5]+4=34
its an absolute value problem

Answer 1

is x-5 the abs value part? ie:
2|x-5|+4=34

Answer 2

yes

Answer 3

We are able to write this as two separate equations if we limit the domain, but first we need to know where to separate it. at what x value does the abs value portion = exactly 0?

Answer 4

not sure. i dont really know how to isolate this varible- what to do with the 2 divide or not..

Answer 5

don't worry about that yet, look at just |x-5|. at what x value will this equation = 0?

Answer 6

5, right

Answer 7

right, so now we know when the absolute value part of the equation flips. so now we need to test each side.
when x=4 and when x = 6 the equation equals 1.
we can see here that when x=6, the x is not changed:
|6-5|=1 && 6-5=1
however when x=4:
|4-5|=1 but 4-5=-1

so from this we can tell that for all x>5, x=x
for all x<5, x=-x

does that make sense so far?

Answer 8

im sorry, x does not equal -x in this one

Answer 9

sort of but i dont get how this has to do with the rest of the problem..

Answer 10

the idea is to turn this one equation into a system of inequalities, ie:
when x>5 then (equation 1)
when x<5 (equation 2)

Answer 11

right, i get that there has to be two outcomes..

Answer 12

actually when x<5, x=((5-x)*2)
and when x > 5, x=x

with this we can make a piece-wise function

Answer 13

but there is an easier way to do it than changing x, i remember now, im sorry

Answer 14

no problem

Answer 15

we can treat |x-5| as parentheses, and just put a negative sign in front, so that it distributes:

x>5:
|x-5| = (x-5)

x<5:
|x-5| = -(x-5)

does this part make sense?

Answer 16

oo i think so

Answer 17

now we have:
x>5 then 2(x-5)+4=34
x<5 then -2(x-5)+4=34 (the negative goes in front of the 2)

Answer 18

right

Answer 19

so now solve for x for both, and make sure it is in the domain, ie:

for the first one, if you get 4 as your x, it is not >5

Answer 20

right so both equations (outcomes)= 30 right?

Answer 21

no, when i solve for x, the first equation x=20, the second x=-10

Answer 22

my book says the answers are 12, and -18..

Answer 23

It looks like i made a mistake somewhere, let me find it.

Answer 24

Check the question that you gave me, because it should be x=-10,20

Answer 25

ya im confused, do you distribute the 2 into the perentices?

Answer 26

you can do it a few ways:
first move over the 4
2(x-5)+4 (-4) = 34 (-4)
2(x-5)=30

you can then either distribute, or divide out 2

Answer 27

ya my bad you got it right -i was looking at a diff answer.

Answer 28

sry about that and thank you sooo much for your help!!

Answer 29

no problem, do you understand it better now?

Answer 30

yup!

Answer 31

Glad I could help, remember to use parentheses for abs value, and then through a negative sign on one of the inequalities to make it work =)