Question

Choose the absolute value inequality that corresponds to the given compound inequality.

–5 < x + 2 < 9

A. |x + 2| < 5
B. |x + 2| < 9
C. |x| < 7
D. |x| < 9

How exactly do I find this, you guys?

Answer 1

First take the first part and simplify it

Answer 2

Take -5<x+2 and simplify

Answer 3

so... it would be -7 < x right? @SandeepReddy

Answer 4

yes exactly

Answer 5

and now do the second part

Answer 6

Do I simplify x + 2 < 9 ?

Answer 7

yes

Answer 8

and thats x < 9

so it would be -7 < x < 9 ?

Answer 9

close....when you simplified x + 2 < 9

it doesn't just become x < 9..it becomes...?

Answer 10

@LilSlim09 you have to simplify x + 2 < 9 , that doesnt get you x<9 right?

Answer 11

Im not sure to be honest.... It wasn't explained to me very well. Do I have to flip the sign?

Answer 12

well lets look what you did for -5 < x + 2

what did you do here?

Answer 13

@johnweldon1993 I added two to -5 and got -7

Answer 14

why u added 2 in specific?

Answer 15

@SandeepReddy because I had to get X by itself

Answer 16

...you subtract 2...from -5....and got -7 right?

you need to get x by itself....so you would subtract 2 from both sides

Answer 17

Same u do to The second part x + 2 < 9

Answer 18

think about it like this

x + 2 > -5

if you add 2 to both sides

x + 4 > -3

not right .....

now when you SUBTRACT 2 from both sides

x + 2 > -5
-2 -2

x > -7

right?

Answer 19

I think so.. So I did have to flip the sign of the second equation.

Answer 20

so now you have

x + 2 < 9

how would you get x by itself here? ***hint...same thing as the other one

Answer 21

so it would be
x+ 2 < 9
-2 -2

x < 7

Answer 22

Yes now see both results

Answer 23

And how will I figure out the question that was asked?

Answer 24

correct!

now put it all together

you have

x > -7
and
x < 7

so write it like

-7<x<7

see how it has both versions of 7 here? both positive AND negative?

this means....?

Answer 25

I have no idea... I know it is like saying x is greater than -7 but less than 7

Answer 26

right.....but think about it.....

if x is greater than -7....and less than +7

that must mean that the absolute value of x would be <7 right?

Answer 27

so the answer is |x| < 7 ?

Answer 28

say I gave you the number -5.......the absolute value of that...is 5....still less than 7

as long as the number is less than 7...the absolute value of the number will satisfy that equation

so yes....that is your answer

Answer 29

thank you so much!