Question

How do I convert an inequality to an inequality with absolute symbols?

Answer 1

Depends, is it descrete?

Answer 2

here's an example....-3 < x < 3

Answer 3

Oh, you mean absolute value..

\[|a| < b \iff -b < a < b\]

Answer 4

The arrows mean that each side (left or right) means the same thing. Anytime you have one, you can write the other instead.

Answer 5

\[\iff\]
Those arrows I mean.

Answer 6

How would I write this equation as an absolute value inequality?

Answer 7

So look at my example.. What do you have that is in the same spot as the 'a' ?

Answer 8

I just gave my example in general terms. you can use any value for a you want, and any value for b you want (as long as \(b \ge 0\))

Answer 9

-b < a < b

In your problem, what is b, and what is a?

Answer 10

- b is less than a...b is great than a..

Answer 11

No, I mean you have a problem in front of you that looks the same, but has numbers instead of a and b. What is the number that corresponds to the b and what is the number that corresponds to the a?

Answer 12

b and a are both 3?

Answer 13

No, b is 3, a is x.

Answer 14

-b < a < b
-3 < x < 3

See the similarity?

Answer 15

So if:

-b < a < b

is the same as this:

|a| < b

Then what would
-3 < x < 3

be the same as?

Answer 16

IxI < 3?

Answer 17

Yep! Nicely done.

And if you had

-4 < f < 4 ?

Answer 18

IxI < 4?

Answer 19

The x would be an f. But yeah.

Answer 20

Here's a little trickier one..

-5 < a+b < 5

Answer 21

Ia + bI < 5?

Answer 22

Yes! awsome.

Also remember you can go the other way..

|b| < g can be written as -g < b < g too.

Answer 23

They mean the same thing.

Answer 24

Can you explain another one? :)

Answer 25

Sure

Answer 26

So how would you simplify |3x| > 27, again?

Answer 27

Ok, so here we are gonna go the other way.

Answer 28

Rewrite it as an inequality without the absolute values

Answer 29

-27 < 3x < 27?

Answer 30

Yes. Now we want to get the x by itself, so what do we do?

Answer 31

Sorry, when I say 'by itself' I mean without the 3 in front of it.

Answer 32

we divide the negative 27 and 27 by 3.

Answer 33

Yes. We divide everything by 3.

Answer 34

the -27, the 3x, and the 27 are all divided by 3 what do we have now?

Answer 35

Are each divided by 3 rather.

Answer 36

leave it as is?

Answer 37

Yeah, we have:

\[-\frac{27}{3} < \frac{3}{3}x < \frac{27}{3}\]
Which simplifies to
\[-9 < x < 9\]
Then we can rewrite in absolute value form again...

Answer 38

actually I just needed to get it into standard inequality form..

Answer 39

Oh, ok well there ya go.

Answer 40

thanks. hopefully this will all stick soon...:)

Answer 41

The only tricky thing to remember is that when you multiply or divide everything by a negative you have to change the direction of the inequality.

Answer 42

I tend to remember that, for some reason..but anyway,thanks again..got to get back to my math. :)

Answer 43

good luck =)