How do you determine when to use addition or subtraction when solving an absolute value inequality using a graph?

- anonymous

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- anonymous

Example:

##### 1 Attachment

- anonymous

I thought distance was always supposed to be negative, but some of the answers to my questions use a positive.

- LynFran

no distance is always positive

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- anonymous

The answers use negatives.

- LynFran

because we are talking about absolute values .... we usually get 2 answers one is positive and one is negative..

- LynFran

@DecentNabeel wat do u think..?

- triciaal

distance is always a positive unit of measure between 2 points

- LynFran

for absolute .... example |x+3|=5
then (x+3)=+5 and (x+3)=-5

- triciaal

one approach to doing absolute value problems is to split in 2 the positive and the negative solve each then find the combined solution

- anonymous

I'm not solving an actual absolute value inequality, I am trying to write absolute value inequalities using a graph.

- triciaal

read again slowly

- triciaal

solve each and put the results on the same graph to see the final solution

- anonymous

There is nothing to solve. I already have the graphs, and am working backwards to find the inequality.

- triciaal

look at number 25

- triciaal

x > -12 and x< -6

- freckles

\[\text{ assume } a \text{ is positive } \\ |x-c| \le a \text{ means we are shading the interval }[ c-a , c+a] \\ |x-c| \ge a \text{ means we are shading everything outside the interval } (c-a,c+a)\]

- triciaal

|dw:1440897882997:dw|

- triciaal

|dw:1440898166918:dw|

- anonymous

I don't need to solve it. The answer was |x+9|<3
I need to know when to use addition or subtraction when solving from a graph.

- freckles

\[
\text{ assume } a \text{ is positive } \\ |x-c| \le a \text{ means we are shading the interval }[ c-a , c+a] \\ |x-c| \ge a \text{ means we are shading everything outside the interval } (c-a,c+a)\]
|dw:1440898355091:dw|
|dw:1440898407502:dw|
I have added drawings in case you didn't understood my words

- freckles

notice in the first graph you put c=-9 and a=3
the second one you have c=1 and a=2

- freckles

i think a couple of my a's above looks like 2's
but they are a's

- freckles

|dw:1440898758376:dw|

- freckles

|dw:1440898823346:dw|
can you guess how to represent this

- anonymous

|x-2|<-5

- freckles

we have open circles so we don't want an equality thing in there at all
we also want a < symbol since our shading is between the numbers
now the first thing to notice is the center number which is -5
that is our c
and a is how far the exterior numbers are away which is 2
|x-(-5)|<2
|x+5|<2

- freckles

|dw:1440899046041:dw|

- anonymous

\[|x-3.5|\le4.5\]

- freckles

let's try another one
|dw:1440899271018:dw|*

- freckles

you are awesome

- freckles

I made a type-o and you still figured out

- freckles

|dw:1440899357439:dw|
yes the center number is 3.5
so you c is 3.5
and 3.5 is 4.5 units from 8
and 3.5 is 4.5 units from -1
so we have
\[|x-3.5| \le 4.5\]

- freckles

|dw:1440899526070:dw|
the center number here is 5
and your a is 1 since both 4 and 6 are 1 unit from 5
\[|x-5| >1\]

- freckles

anyways do you have any questions?

- anonymous

But how do you know when to write the inequality as a negative or a positive?

- freckles

what do you mean

- anonymous

Like, you had |x-5|>1 and |x+5|<2
How do you know when to put negative and positive

- freckles

we only had |x-5|>1 for previous one

- anonymous

Yes, but how did you know to put a negative.

- freckles

|x-(-5)|>1
would be right if -5 was at the center
and to the right you had -5+1
and to the left you had -5-1
instead

- freckles

|x-5|>1
means
x-5<-1 or x-5>1
which means
x<4 or x>6
|dw:1440899857523:dw|

- freckles

|x-5|>1 looks like this:
|dw:1440899886515:dw|
while
|x-(-5)|>1 looks like this:
|dw:1440899916458:dw|

- freckles

by the way |x-(-5)|>1
is the same as saying |x+5|>1
since -(-5)=+5

- freckles

|x-c|<=a
says we want all numbers a units away from c in both directions

- freckles

and yes c can be a positive or negative number

- anonymous

Ohhhhh! I finally understand!

- anonymous

Thanks for your help!

- freckles

np

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