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anonymous
 one year ago
Graph and solve :)
anonymous
 one year ago
Graph and solve :)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439059109467:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.1first step is add +3 to both sides

phi
 one year ago
Best ResponseYou've already chosen the best response.1you 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
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439059343639:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes you could also write it this way \[x1 3 + 3 \le 1+4 \\ x1 \le 4 \] the   mean absolute value. if what is "inside" is positive, you can ignore them for the moment, assume x1 is 0 or bigger (i.e. positive) then we have \[ x1 \le 4 \] now what should you add to both sides to get "x by itself" ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok now we assume x1 is negative inside the   the absolute value signs will make it positive this part is a bit tricky to see (maybe?) but if (x1) is negative, and we multiply it by 1 we will make it positive in other words *assuming x1 is negative* then  x1 is the same thing as 1*(x1) and we can write \[ 1\cdot (x1) \le 4 \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, now add 1 to both sides

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but u cant add a 1x to 4 right? Bc they r different terms

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes. 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
 one year ago
Best ResponseYou've already chosen the best response.0Alright, thanks:) How do ya graph that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Also, wouldnt the sign change since it was divided by a 1??

phi
 one year ago
Best ResponseYou've already chosen the best response.1relations 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
 one year ago
Best ResponseYou've already chosen the best response.13 <= 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
 one year ago
Best ResponseYou've already chosen the best response.0Thanks, how do I graph that on a line?

phi
 one year ago
Best ResponseYou've already chosen the best response.1make 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439060288511:dw like this?

phi
 one year ago
Best ResponseYou've already chosen the best response.1the 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
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439060533573:dw That way?

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, 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
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439060648200:dw Like that?

phi
 one year ago
Best ResponseYou've already chosen the best response.1you 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
 one year ago
Best ResponseYou've already chosen the best response.0Ohhh! Thanks so much for all your help:)))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im going to post another in the open question section, so if u want to help again...:)
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