Question

math homework help?
|y+4| < 1

a. -5 < y < -3
b. -3 < y < 5
c. -4 < y < 1
d. 1 < y < 4

Answer 1

First you need to save the problem on the top. Do you know how to do that?

Answer 2

Well you need to put it into absolute value right?

Answer 3

It becomes two inequalities.

Answer 4

It is in absolute value

Answer 5

\[
y+4<1
\]and \[
-(y+4)<1
\]

Answer 6

then you subtract 4?

Answer 7

Yes, for the first formula.

Answer 8

and the second one you distribute the negative?

Answer 9

You can, or you can divide out \(-1\) on both sides.

Answer 10

Generally you want to do the operation outside of the parenthesis first when isolating variables.

Answer 11

so -y - 4 < 1

Answer 12

yes

Answer 13

and you add 4 to get y = -5 and in the first equation y = -3

Answer 14

There is no equals sign.

Answer 15

would that mean it's a?

Answer 16

For the first inequality, we would get: \[
y<-3
\]

Answer 17

For the second inequality we start at: \[
-(y+4)<1
\]Then we add \(y+4\) to both sides.\[
0 < 1+y+4
\]

Answer 18

Then we subtract the parts that aren't \(y\)\[
-5<y
\]

Answer 19

Does this make sense?

Answer 20

i think so.. -5 < y < -3 right?

Answer 21

Yes.

Answer 22

okay thank you :)

Answer 23

But could you do it on your own next time?

Answer 24

yes

Answer 25

!(-5) +4 ! < 1
!-1! < 1
!1! < 1
1 < 1 not true

Answer 26

That is why it is \(-5<y\) and not \(-5\leq y\).

Answer 27

!(-3)) + 4 ! < 1
!1 ! <1
not true

Answer 28

i got 100% thank you so much!

Answer 29

We did not say that \(y=-3\) or \(y=-5\). It must be between.

Answer 30

! (-4) + 4! < 1
!0)! < 1 true

Answer 31

!(1) + 4! < 1
!(5) < 1
not true
so answer is c

Answer 32

i got it right when i chose a

Answer 33

If you chose a : -5 < y < -3
then !y + 4! < 1 is
! (-5) + 4! < 1
! -1! < 1
!(-1)! is 1
so 1 < 1 which is not true.
so you would have got the answer wrong

Answer 34

well i got it right :) sorrry