Question

A snack food company packages bags of chips. The bag of chips must weigh within .4 ounces of the labeled weight. If the company is packaging bags of chips that are labeled 10 ounces, write an absolute value inequality that represents the acceptable actual weights of the bags.

Answer 1

Ok, so first, we want the absolute difference between a bag of chips weighing x ounces and the labeled weight, 10 ounces. So, this is just:\[\left| x-10 \right|\]

Now, we need to add in the inequality to ensure that absolute difference is less than 0.4 ounces. Give it a try?

Answer 2

So do we subtract?

Answer 3

I'm not sure what you mean. Subtract to do what?

Answer 4

x-10 is already a subtraction. We cannot simplify this any further, however, because x is a variable.

Answer 5

So do i add 0.4 to 10 ounces?

Answer 6

Note that absolute difference means this: |3-1|=2, and |1-3|=|-2|=2

Answer 7

Not quite. I want you to start off with the inequality. What must |x-10| be less than?

Answer 8

It equals x-10 right?

Answer 9

The difference in weight between the bag of chips and the label is |x-10|, e.g., if the bag weighs 9 ounces it is |9-10|=|-1|=1

Answer 10

i'm so confused

Answer 11

Ok. First, we're saying that a bag of chips actually weighs x ounces. That means, its unknown -- it's a variable. Are you ok with this part?

Answer 12

yes

Answer 13

Ok, so what does |x-10| mean?

Answer 14

its an absolute value

Answer 15

Yes, absolute value of what?

Answer 16

x-10 right?

Answer 17

Yes, and in English, that means "the absolute difference in ounces between the weight of the bag of chips and its labeled weight".

Answer 18

So, we want this absolute difference in weight to be less than 0.4 ounces, right?

Answer 19

Yes

Answer 20

So is it? |10 + x| ≥ 0.4

Answer 21

\[\left| x-10 \right| < ?\]

Answer 22

0.4

Answer 23

Yes, |x-10|<0.4

Answer 24

The different in their weights must be less than 0.4 ounces for it to be acceptable. Otherwise, it is unacceptable.

Answer 25

Another way of saying that is, x must be in the range [9.6, 10.4].

Answer 26

Well, actually, (9.6, 10.4), since we are using < rather than <=

Answer 27

|10 + x| ≤ 0.4

Answer 28

No, |10+x| is not a difference. We want a difference.

Answer 29

We actually already arrived at the answer: |x-10|<0.4

Answer 30

ohhh difference subtraction sorry i'm getting side tracked |10 - x| ≤ .04

Answer 31

Except .04 should be 0.4, probably a typo.

Answer 32

yea it is sorry

Answer 33

Also, note that |10-x|=|x-10|. I only mention this in case you didn't know.

Answer 34

|10 - x| ≥ .04

Answer 35

Nope, you already answered it correctly. |10-x|<0.4

Answer 36

But thats not one of the answers

Answer 37

|10-x|>0.4 would tell us which bags of chips are unacceptable. We want it to tell us which bags of chip are acceptable, which is just when they satisfy the inequality, |x-10|<0.4

Answer 38

Oh, it's multi-choice?
Show me.

Answer 39

A. |10 + x| ≥ 0.4
B. |10 - x| ≥ .04
C. |10 + x| ≤ 0.4
D. |10 - x| ≤ .04

Answer 40

You there?

Answer 41

Sorry, yes I'm here.Let me have a look.

Answer 42

I'm at a loss. None of those choices look correct.

|10-x|<=0.4 should be the answer. Are you sure .04 isn't a typo?

Answer 43

@mrgenius

Answer 44

What do you think about those multi-choice options, mrgenius? I think she must have typed .04 when she actually mean 0.4

Answer 45

i think its 0.04...not a typo. looks like a tricky question.. hang on

Answer 46

im lost

Answer 47

LOL, I think it was a typo on her part.

Answer 48

0.4/10=0.04