- anonymous

Graph and solve :)

- chestercat

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- anonymous

|dw:1439059109467:dw|

- anonymous

- phi

first step is add +3 to both sides

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## More answers

- anonymous

4

- phi

you have a "relation" and you must do the same thing to both sides
after you add +3 to both sides, what is the new relation?

- anonymous

|dw:1439059343639:dw|

- phi

yes
you could also write it this way
\[|x-1| -3 + 3 \le 1+4 \\ |x-1| \le 4 \]
the | | mean absolute value. if what is "inside" is positive, you can ignore them
for the moment, assume x-1 is 0 or bigger (i.e. positive)
then we have
\[ x-1 \le 4 \]
now what should you add to both sides to get "x by itself" ?

- anonymous

x<5

- phi

ok
now we assume x-1 is negative inside the | |
the absolute value signs will make it positive
this part is a bit tricky to see (maybe?)
but if (x-1) is negative, and we multiply it by -1 we will make it positive
in other words *assuming x-1 is negative*
then | x-1| is the same thing as -1*(x-1)
and we can write
\[ -1\cdot (x-1) \le 4 \]

- anonymous

so -1x+1<4 ??

- phi

yes,
now add -1 to both sides

- anonymous

but u cant add a -1x to 4 right? Bc they r different terms

- anonymous

-1x<3

- phi

yes. just add -1 to both sides
ok, now you have -x <= 3 (the <= means less than or equal in case you can't type \(\le\))

- anonymous

Alright, thanks:) How do ya graph that?

- anonymous

Also, wouldnt the sign change since it was divided by a -1??

- phi

relations with negative numbers are tricky.
*if* we multiply by -1 (on both sides) we have to "flip" the relation
however, if we only add or subtract we don't have to worry about that rule
we could add +x to both sides
-x <= 3
-x + x <= 3 + x
0 <= 3 + x
now add -3 to both sides
-3+0 <= 3 - 3 + x
and finally
-3 <= x

- phi

-3 <= x
means x is equal to or bigger than -3
the other relation (see up above) x<= 5
means x is 5 or smaller
both have to be true for the original relation
\[ | x -1| - 3 \le 1\]
people often write the answer in short form like this\[ -3 \le x \le 5 \]

- anonymous

Thanks, how do I graph that on a line?

- phi

make a number line with numbers from -3 to 5
put a solid (filled in) circle at -3 and at 5 (this means x could be -3 or -5)
and draw a solid line connecting the dots to show x could be any number in between

- phi

*could be -3 or +5

- anonymous

|dw:1439060288511:dw|
like this?

- phi

the arrow on the left side is pointing to numbers smaller than -3 (example -4, -5)
the answer are \( -3 \le x \)
notice the "big" side of the \( \le\) is next to x , which is a clue x is bigger than the other side (the -3)
in other words , you want to show that numbers bigger than -3 (such as -2 , -1, 0, etc)
are the answer.

- anonymous

|dw:1439060533573:dw| That way?

- phi

yes, and of course, \( x\le 5\) means x is smaller (notice the small pointy end of the \(\le\) is next to x , which is a clue x is smaller than the "big" side (which has 5)

- anonymous

|dw:1439060648200:dw| Like that?

- phi

you want your graph to show which numbers make the problem "true"
I would leave off the arrow tips because people might interpret that to mean the answer goes forever in that direction.
in other words, they would expect just
|dw:1439060715000:dw|

- anonymous

Ohhh! Thanks so much for all your help:)))

- anonymous

im going to post another in the open question section, so if u want to help again...:)

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