Question

When packing a sultcase for a trip, the optimal welght of the suttcase Is 40 pounds. You aim for this weight with every trip you take. But your
sultcase's actual welght tends to vary by at most a certain number of pounds.

Part A. Write an absolute value inequality that models this relationship.

Part B. If the suitcase weight can vary by at most 7.5 pounds,what inequality can be used to find the range of acceptable weights for your suitcase?

Part C. Use the inequality from part B to determine the range of acceptable weights for the suitcase.

Part E. How would the inequality in part B change if you wanted to know the rate of weights that are unacceptable for your suitcase? Explain.

Part F. What is the solution for the inequality you created in part E?

Part H. What comparisons can you make between the two inequalities?

Part I. Will there ever be an instance where there is no solution to an absolute inequality? If yes,then what would the inequality look like?

Answer 1

Answer:

|x − 40| ≤ 7.5.

Step-by-step explanation:

The absolute value inequality |x − 40| ≤ y models the relationship between the acceptable weights of the suitcase and the amount it can vary.

If the suitcase weight can vary up to 7.5 pounds, then 7.5 can be substituted for y in the inequality:

|x − 40| ≤ 7.5.

This inequality can be used to find the range of acceptable weights of the suitcase.