Question

The ideal width of a safety belt strap for a certain automobile is 6 cm. An actual width can vary by at most 0.4 cm. Write an absolute value inequality for the range of acceptable widths. Picture of possible answers included.

Answer 1

so, what is the possible lenghh's minimum?

Answer 2

sorry width**

Answer 3

what is the smallest the strap can be?

Answer 4

The smallest it can be is 0.4 cm, right?

Answer 5

@mathstudent55 Do you think you'd possibly be able to assist me with this?

Answer 6

" 6 cm. An actual width can vary by at most 0.4 cm." Vary means, + or -

Answer 7

does that make sense?

Answer 8

Yeah I guess

Answer 9

ok so, what is the max width?

Answer 10

It has to be six...Because 0.4 cm is less than 6..

Answer 11

hmm ok, let me try and explain using something practical to you

Answer 12

do you play sports do cheerleading or any team activity?

Answer 13

Nope

Answer 14

ok, how about makeup?

Answer 15

noo, I'm a boy, haha.

Answer 16

ok, uhm, then tell me something that you like that you deal with daily?

Answer 17

$$\Huge 6cm \pm 0.4cm$$\$$\Huge \text{means } 6 +0.4\text{ or }6-0.4$$

Answer 18

^^ Alright..

Answer 19

I'm sorry, I'm just rubbish at math in every possible way.

Answer 20

that would be why I am trying to make a real world thing. So do you eat?

Answer 21

Yes

Answer 22

ok, so you always have pizza on friday nights

Answer 23

how many slices you eat varies by about 2 slices. Usually if you are just hungry you will eat 4 slices let's say

Answer 24

but if you are super hungry, can you tell me how many slices you would have?

Answer 25

6

Answer 26

yes, and if you are not really hungry, how many?

Answer 27

4?

Answer 28

well, how many sllices do you usually have?

Answer 29

4..

Answer 30

ok, so if you are not as hungry as usual

Answer 31

Then like 2 I'd guess..

Answer 32

yes

Answer 33

so what you did there was find the absolute minimum number of slices you would eat, 2, and the absolute maximum number of slices, 6

Answer 34

so, now, how did you find 2? what did you do?

Answer 35

I didn't do anything to find 2..?

Answer 36

you didn't?

Answer 37

ok, how did you get 6 then?

Answer 38

I don't understand what you're asking..All I know is that 2 is the minimum and 6 is the maximum..

Answer 39

but how did you get those? when I asked you, how did you determine that the most slices you would eat would be 6?

Answer 40

The range of acceptable widths is 5.6 cm to 6.4 cm $$\Huge |w-6| \le 0.4$$
sub in 6.4 for w will give |6.4 - 6|<=0.4 which is a true statement.

sub in 5.6 for w will give |5.6 - 6| <= 0.4 which is also a true statement.

Therefore all the values between 5.6 and 6.4 will give a true statement.

This makes this absolute value inequality the correct answer for acceptable widths.

Answer 41

Any questions @brandonfrabel ?