Acompany 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 mixes?
a. x < 9.02 or x > 9.48 because |x − 0.23| + 9.25 > 0
b. x < 9.25 or x > 9.48 because |x − 9.25| > 0.23
c. x < 9.25 or x > 9.48 because |x − 0.23| + 9.25 > 0
d. x < 9.02 or x > 9.48 because |x − 9.25| > 0.23

d. x < 9.02 or x > 9.48 because |x − 9.25| > 0.23

Step-by-step explanation:

Given,

The standard weight of the pack = 9.25 oz,

The pack must weigh within 0.23 oz of the target weight to be accepted.

i.e. if x represents the weight of the pack,

If x > 9.25 oz

then x - 0.925 ≤ 0.23  (1)

if x < 9.25

then 9.25 - x ≤ 0.23

⇒ -(x-9.25) ≤ 0.23   (2)

From equation (1) and (2),

The accepted range of mass is,

|x-9.25| ≤ 0.23

Hence, the rejected range mass would be,

|x-9.25| > 0.23

⇒ x - 9.25 > 0.23 or -x + 9.25 < 0.23

⇒ x > 0.23 + 9.25 or -x > 0.23 - 9.25

⇒ x > 9.48 or - x > −9.02

⇒ x > 9.48 or  x < 9.02

the value of x is 28.2