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solve the 2 inequalities (1/3)x + 4 > 1 and (1/3)x + 4 < -1
wait the sign changes for the neg 1?
Think about what absolute value means: it's the DISTANCE from 0. So if |z|>3, then there are TWO ways that can happen.... either z is more than 3 units TO THE LEFT OF 0 or it is more than 3 units TO THE RIGHT of 0. Either way makes it true... so I can rewrite: |z|>3 as ---> z<-3 OR z>3 Notice that it's a "compound inequality", with an OR in the middle. So you have a "2 part" solution set.
if: |something|>a where a is some positive number, then the "something" is AT LEAST a units from 0, so: something<-a OR something>a
wait so can u show me how to do the two....
If you can wrap your head around abs value as the distance from 0, a lot of these abs value problems can become much more intuitive to set up and solve. :)
oh wait i get it
NO don't try to solve it with the abs value there! You have to first REWRITE IT as 2 separate, compound inequalities that DON'T INVOLVE ABSOLUTE VALUE. THEN you'll be able to solve each of them as usual.
ill solve it and ill make sure of the answer with u
yeah i know.
That is what cwrw238 was getting at above, although I would take issue with the word "AND" between the inequalities. It should be OR in this case, and that's in important distinction, because the "stuff" inside the | | is AT LEAST 1 unit from 0. So that "stuff" is EITHER to the right of 1, or to the left of -1.
wait do i have to simplify more?
so would it be x>-9 or x<-15
You have a sign problem.. the x<-15 is correct, but double-check your work on the other part....
Oh wait, NEVER MIND!
That is correct. :)
my bad. lol
So you see how it's a 2-part solution set. If you are doing interval notation and set unions & intersections, you would write this one as a UNION of 2 sets. But if not, the inequality notation for the solution set should be fine too. :)
you're welcome. :)
I have a world problem
Golfing: You plan on going this weekend with a friend. You can either go to your favorited course which is 14 miles north of your house or to your friends favorite course which is 14 miles south of your house. Write an absolute value inequality that represents all the distacnes you may be from your house.
I'm not entirely sure what this is getting at... obviously the maximum distance from your house is 14 miles. But maybe if you consider the north to be a "positive" direction and south to be a "negative" direction, then you can say that the distance d is such that: -14
so the answer would be -14