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
x < 9.02 or x > 9.48 because |x − 9.25| > 0.23
The correct answer is: x < 9.02 or x > 9.48 because |x − 9.25| > 0.23.
The correct answer is option: x < 9.02 or x > 9.48 because |x - 9.25| > 0.23.
To determine the range of rejected masses for the manufactured trail mixes, we need to consider the acceptable weight range for each pack. The target weight is 9.25 oz, and the acceptable weight range is within 0.23 oz of the target weight.
To represent the acceptable weight range, we use the absolute value function to calculate the difference between the actual weight (x) and the target weight (9.25). If the difference is greater than 0.23, the pack is rejected.
So the inequality representing the acceptable weight range is |x - 9.25| > 0.23.
To find the range of rejected masses, we can rearrange the inequality using algebraic operations. First, take the absolute value away by splitting it into two inequalities:
1. x - 9.25 > 0.23
2. -(x - 9.25) > 0.23 (note the negative sign)
Simplify each inequality:
1. x > 9.25 + 0.23 = 9.48
2. -x + 9.25 > 0.23
-x > -9.02
x < 9.02 (remember to flip the inequality sign when multiplying by a negative number)
Combining the inequalities, we have:
x < 9.02 or x > 9.48
Therefore, the range of rejected masses for the manufactured trail mixes is x < 9.02 or x > 9.48.