first step is add +3 to both sides
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?
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" ?
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 \[ -1\cdot (x-1) \le 4 \]
so -1x+1<4 ??
yes, now add -1 to both sides
but u cant add a -1x to 4 right? Bc they r different terms
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 \(\le\))
Alright, thanks:) How do ya graph that?
Also, wouldnt the sign change since it was divided by a -1??
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
-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\[ -3 \le x \le 5 \]
Thanks, how do I graph that on a line?
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
*could be -3 or +5
|dw:1439060288511:dw| like this?
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.
|dw:1439060533573:dw| That way?
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)
|dw:1439060648200:dw| Like that?
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|
Ohhh! Thanks so much for all your help:)))
im going to post another in the open question section, so if u want to help again...:)