Question

A company did a quality check on all the packs of trail mix it manufactured. Each pack of trail mix is targeted to weigh 9.25 oz. A pack must weigh within 0.23 oz of the target weight to be accepted. What is the range of rejected masses, x, for the manufactured trail mix?

x < 9.02 or x > 9.48 because |x – 0.23| + 9.25 > 0
x < 9.25 or x > 9.48 because |x – 9.25| > 0.23
x < 9.25 or x > 9.48 because |x – 0.23| + 9.25 > 0
x < 9.02 or x > 9.48 because |x – 9.25| > 0.23

Answer 1

Well, the package is REJECTED if the DIFFERENCE between the weight of the package, x, and 9.25, is MORE than 0.23, right?

So first, think about how to set up THAT condition, as absolute value. If x is either more than 0.23 oz OVER or UNDER the weight of 9.25, then the "distance" of x from 9.25 is GREATER than 0.23, right?

So that will give you an abs value inequality with a ">". E.g.:

|{something}|>0.23 where a is some positive number.

Now, how does |{something}| get to be greater than 0.23? Remember, what it really means: it means that the DISTANCE of the {something} from 0 is more than 0.23.

So if {something} is MORE THAN 0.23 units from 0, then either:

{something} is more than 0.23 units to the RIGHT of 0
......... which means that {something} > 0.23
OR
{something} is more than 0.23 units the LEFT of 0
.......... which means that {something} <-0.23

So combine these into a compound equation:
{something} > 0.23 OR {something} <-0.23

Where the {something} is whatever was INSIDE the absolute value. Then solve each of those equations to get your solution "ranges" for x.

Answer 2

i hope that helped a little bit >_<

Answer 3

So whats the answer i never concentrate when i read it's my condition

Answer 4

x < 9.02 or x > 9.48 because |x - 9.25| > 0.23 :)

Answer 5

Thank you so much :)

Answer 6

no problem. anytime:)