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 mixes?

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

9.25 - 0.23 = 9.02 (It can't weigh less then this)
9.25 + 0.23 = 9.48 (It can't weigh more then this)

rejected masses are : x < 9.02 and x > 9.48

D) x < 9.02 or x > 9.48 because |x − 9.25| > 0.23

Answer 2

The correct option is D) x < 9.02 or x > 9.48 because |x − 9.25| > 0.23

Explanation:

Given:- 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.

We need to find out the correct range of rejected masses, X for the manufactured trail mixes

9.25 - 0.23 = 9.02 (It can't weigh less then this)

9.25 + 0.23 = 9.48 (It can't weigh more then this)

Since, rejected masses are : x < 9.02 and x > 9.48

Only option A and D has condition x < 9.02 and x > 9.48

In option A) |x − 0.23| + 9.25 > 0

this is wrong condition because it must be |x − 0.25|

For Option D)

Check:

modulus |x − 9.25| > 0.23 express as

- 0.23 > (x − 9.25) > 0.23

Add 9.25 in above ,

- 0.23 + 9.25 > (x − 9.25 + 9.25) > 0.23 +9.25

9.02 > x > 9.48

True

So, the correct option is D)

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