Solve the inequality!!

- Ammarah

Solve the inequality!!

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- Ammarah

|dw:1378067469429:dw|

- cwrw238

solve the 2 inequalities
(1/3)x + 4 > 1
and (1/3)x + 4 < -1

- Ammarah

wait the sign changes for the neg 1?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- DebbieG

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.

- DebbieG

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

- Ammarah

oh

- Ammarah

|dw:1378067830772:dw|

- Ammarah

wait so can u show me how to do the two....

- DebbieG

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. :)

- Ammarah

oh wait i get it

- DebbieG

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.

- Ammarah

ill solve it and ill make sure of the answer with u

- Ammarah

yeah i know.

- DebbieG

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.

- Ammarah

|dw:1378068011854:dw|

- Ammarah

wait do i have to simplify more?

- Ammarah

so would it be x>-9 or x<-15

- DebbieG

You have a sign problem.. the x<-15 is correct, but double-check your work on the other part....

- DebbieG

Oh wait, NEVER MIND!

- DebbieG

That is correct. :)

- DebbieG

my bad. lol

- DebbieG

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. :)

- Ammarah

ok thanks.

- DebbieG

you're welcome. :)

- Ammarah

I have a world problem

- Ammarah

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.

- DebbieG

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

- Ammarah

so the answer would be -14

Looking for something else?

Not the answer you are looking for? Search for more explanations.