Question

a manufacturer uses a machine to fill bags with 13 ounces of chocolate, modeled by the equation |w - 13| = 0.6, where w is the weight of chocolates in ounces. what are the lowest and highest weights according to the model?
options:
12.4 and 13.6 ounces
12.4 and 19.6 ounces
7.6 and 13.6 ounces
7.6 and 19.6 ounces

Explanation:

Step1: Solve the absolute value equation

The equation is \(|w - 13| = 0.6\). By the definition of absolute value, this means \(w - 13 = 0.6\) or \(w - 13 = -0.6\).

Step2: Find the two solutions

For \(w - 13 = 0.6\), add 13 to both sides: \(w = 13 + 0.6 = 13.6\).
For \(w - 13 = -0.6\), add 13 to both sides: \(w = 13 - 0.6 = 12.4\).

Answer:

12.4 and 13.6 ounces (corresponding to the first option: 12.4 and 13.6 ounces)