To determine the acceptable weight of a 16-ounce bag of sugar within a variance of 0.4 ounces, we should set up an absolute value inequality. Here's the step-by-step reasoning process:
1. Understanding the Problem:
- The nominal weight of the bag of sugar is 16 ounces.
- The acceptable variance allowed is up to 0.4 ounces, which means the weight can be either 0.4 ounces more or 0.4 ounces less than 16 ounces.
2. Representing the Range Mathematically:
- If [tex]\( x \)[/tex] represents the actual weight of the bag, then [tex]\( x \)[/tex] should be within the range of 16 ± 0.4 ounces.
- This means [tex]\( x \)[/tex] should lie between 15.6 ounces (16 - 0.4) and 16.4 ounces (16 + 0.4).
3. Absolute Value Inequality:
- The absolute value expression that best represents the allowable deviation from 16 ounces is [tex]\( |x - 16| \)[/tex].
- To express that the deviation [tex]\( |x - 16| \)[/tex] should be at most 0.4 ounces, we write the inequality [tex]\( |x - 16| \leq 0.4 \)[/tex].
Therefore, the absolute value inequality which can be used to find [tex]\( x \)[/tex], the acceptable weight of a bag of sugar, is:
[tex]\[ |x - 16| \leq 0.4 \][/tex]
The correct answer is:
B. [tex]\( |x - 16| \leq 0.4 \)[/tex]
