Question

=

Answer 1

yes

Answer 2

that was the same question you did a few days ago.

Answer 3

*A U B

Oh yah I just got confused on what I wrote for two of them, so I wanted to make sure

Answer 4

yes to Reals
rationals and irrationals together are all real numbers

Answer 5

But I also had one I was having trouble with.

Write a compound inequality to represent all of the numbers between -4 and 6.

Answer 6

one way to start is pick a number that is between them (example: 0)
what is the inequalities you can write using 0 and those 2 numbers ?

Answer 7

1?

Answer 8

I was thinking you could write
-4 < 0
and 0< 6

or
-4 < 0 < 6
to make that any number between -4 and 6, replace 0 with x
-4 < x < 6

the idea is that any number between -4 and 6 on the number line will be bigger than -4 and less than 6

Answer 9

Yah I was really confused on this question. I know this may sound stupid, but what's a compound inequality? My course never defines terms, it just starts using them :(

Answer 10

compound means
n. (kŏm′pound′)
1. A combination of two or more elements or parts. See Synonyms at mixture.

it means more than 1 inequality

Answer 11

in this case
Write a compound inequality to represent all of the numbers between -4 and 6.
we have to use two inequalities:

-4 < x and x < 6
(just one of them would not give us the right answer...we need both)

Answer 12

Oh okay so the first one to show that its less than -4 and the second one to show that its less than 6

Answer 13

you mean bigger than -4

Answer 14

< = less than?

Answer 15

-4 < x means -4 is less than x or x is bigger than -4 (same thing)
the pointy end points at the smaller value
the "fat" end is next to the bigger value.

you would read -4 < x as "-4 is less than x"

Answer 16

but if you see
-4 < x < 6
it is often pronounced: " x is between -4 and 6" or
" x is greater than -4 and less than 6"

(you could say "-4 is less than x and x is less than 6" but that sounds confusing)

Answer 17

So -4 < x < 6 is not equivalent to -4 < x and x < 6

Answer 18

it IS equivalent.

Answer 19

oh

Answer 20

I think I understand

Answer 21

thank you

Answer 22

yw

Answer 23

Just to be sure, i'm putting -4 < x < 6 for my answer, right?

Answer 24

I would write it the way your book has been writing it.
you could write it like this:
{x | x > -4} ∩ {x | x < 6}
(copying from your earlier problem)
or

x > -4 and x < 6

or

-4 < x and x < 6

or

-4 < x and 6 > x

or
-4 < x < 6

Answer 25

obviously -4 < x < 6
is shorter than the other ways.