Question

help please! i will medal!
A company did a quality check on all the packs of nuts it manufactured. Each pack of nuts is targeted to weigh 18.25 oz. A pack must weigh within 0.36 oz of the target weight to be accepted. What is the range of rejected masses, x, for the manufactured nuts?

A) x < 17.89 or x > 18.61 because |x - 18.25| > 0.36

B) x < 17.89 or x > 18.61 because |x - 0.36| + 18.25 > 0

C) x < 18.25 or x > 18.61 because |x - 18.25| > 0.36

D) x < 18.25 or x > 18.61 because |x - 0.36| + 18.25 > 0

Answer 1

If x is the mass of some unknown nut, then x-18.25 is the distance from the target mass of 18.25 oz

Make this distance positive (since negative distance makes no sense) to get |x-18.25|

Answer 2

Now if x = 18.25, then |x-18.25| becomes |18.25-18.25| = |0| = 0

so that distance is 0 (ie we're right on target)

if x was say x = 20, then |x-18.25| = |20 - 18.25| = |1.75| = 1.75

that distance, or error, is 1.75 oz

we're off by 1.75 oz if x = 20

Answer 3

the same can be done with values below 18.25, say x = 15

|x-18.25| = |15 - 18.25| = |-3.25| = 3.25

now we're off by 3.25 oz

Answer 4

the values of x that we want (or accept) are ones that make |x-18.25| equal to 0.36 or less than 0.36

in other words, the distance or error must be at most 0.36. This is the max tolerated error we're accepting

Answer 5

so we accept values of x that make |x-18.25| <= 0.36 true

flip this around to get |x-18.25| > 0.36 and that represents all of the x values we reject because they are too far from 18.25

Answer 6

solving |x-18.25| > 0.36 for x will give you the two boundaries that tell you how far you can go (when you change from acceptance to rejection)

Answer 7

so it's A or C

Answer 8

correct

Answer 9

do you know how to solve |x-18.25| > 0.36 for x?

Answer 10

i get what you explain thank you for that but i dont get the beginning either the 17.89

Answer 11

and no i dont know how to do that

Answer 12

it turns out that if you have something of the form |x| > k for some positive number k, then it breaks down into the following

x < -k or x > k

Answer 13

so what that means in this case,

|x-18.25| > 0.36

breaks down into the two following inequalities

x-18.25 < -0.36 or x-18.25 > 0.36

Answer 14

solve each of them and tell me what you get

Answer 15

ok one second

Answer 16

alright

Answer 17

x<18.61 or x<17.89

Answer 18

@jim_thompson5910

Answer 19

very good,

x-18.25 < -0.36 or x-18.25 > 0.36

x < -0.36+18.25 or x > 0.36+18.25

x < 17.89 or x > 18.61

Answer 20

I got the same thing, just in a different order

Answer 21

oh and you should have x > 18.61 not x < 18.61

Answer 22

oh yeah i read it too fast

Answer 23

that's alright

Answer 24

so A

Answer 25

correct

Answer 26

thank you for the help you help me a lot

Answer 27

you're welcome