Question

[5.02] 16 < 2x + 4 < 4 can someone help me solve. (Without giving the answer).

Answer 1

Similar example

-22 < 2x + 6 < 14

-22-6 < 2x + 6 -6< 14-6 ... Subtract 6 from all sides.

-28 < 2x < 8 ... Combine like terms.

-28/2 < 2x/2 < 8/2 ... Divide all sides by 2.

-14 < x < 4 ... Reduce


So the solution is
-14 < x < 4

Note: this is NOT the answer to your problem since this is a similar example problem

Answer 2

16<2x+4<4

16-4 < 2x+4-4 < 4-4

12 < 2x

12/2 < 2x/2

6 < x

Is this correct?

Answer 3

what happened on step 3?

Answer 4

and is that 16 really positive?

Answer 5

do i make the 16 negative or is it positive in the original question?\

Answer 6

i'm just asking if 16 is positive in the original question

Answer 7

or is it negative?

Answer 8

yes it is positive.

Answer 9

ok, it might make it easier if we let

z = 2x+4

so

16 < 2x + 4 < 4

is the same as

16 < z < 4

Answer 10

do you see a problem here?

Answer 11

not really

Answer 12

z is some number

so

16 < z < 4

says


16 < some number < 4

Answer 13

ok

Answer 14

see the problem now?

Answer 15

the z or some number.

Answer 16

??

Answer 17

16 < z < 4

says

"z is some number between 16 and 4....ie, its greater than 16 AND less than 4 at the same time"

see the problem now?

Answer 18

sorta

Answer 19

can you name any numbers that are greater than 16 AND less than 4 at the same time?

Answer 20

ummm well wouldnt you have to graph both starting at 4 shading right and 16 shading left.

Answer 21

im not good at inequalitys at all

Answer 22

think of a number greater than 16

Answer 23

17

Answer 24

is that less than 4?

Answer 25

nope

Answer 26

what about 18?

Answer 27

stilll over

Answer 28

and 19?

Answer 29

still over

Answer 30

so are there any numbers that are greater than 16 and less than 4?

Answer 31

no

Answer 32

so

16 < z < 4

is not possible, agreed?

Answer 33

agreed

Answer 34

by extension

16 < 2x+4 < 4

is also not possible

Answer 35

since z = 2x+4

Answer 36

ok

Answer 37

so there are no numbers that can replace 'x' and make

16 < 2x+4 < 4

a true inequality

Answer 38

ok

Answer 39

does that make sense?

Answer 40

well yes because oof the 16 and 4 part

Answer 41

alright that's great

Answer 42

ok