Answer :
To solve this problem, we want to determine the acceptable weight range for a suitcase based on given rules. The rule specifies that the weight of the suitcase can vary by at most [tex]\(7.5\)[/tex]. So, the weight is allowed to fluctuate up to [tex]\(7.5\)[/tex] units above or below its current weight, [tex]\(x\)[/tex].
Let's break this down step-by-step:
1. Understand the Concept of Variation: The suitcase's weight can vary by [tex]\(7.5\)[/tex] units. This means:
- The minimum acceptable weight is [tex]\(x - 7.5\)[/tex].
- The maximum acceptable weight is [tex]\(x + 7.5\)[/tex].
2. Representing the Range Mathematically:
- We can use inequalities to express this range. The actual weight of the suitcase, which we'll call [tex]\(weight\)[/tex], can be between these two calculated limits.
- Thus, the inequalities representing this range are:
- [tex]\(x - 7.5 \leq weight\)[/tex]
- [tex]\(weight \leq x + 7.5\)[/tex]
3. Putting it All Together:
- By combining these expressions, we can say that the suitcase weight is acceptable if it satisfies both inequalities:
- [tex]\(x - 7.5 \leq weight \leq x + 7.5\)[/tex].
This step-by-step explanation provides the framework to understand and determine the acceptable weight range of a suitcase based on the described rule of variation by [tex]\(7.5\)[/tex] units.
Let's break this down step-by-step:
1. Understand the Concept of Variation: The suitcase's weight can vary by [tex]\(7.5\)[/tex] units. This means:
- The minimum acceptable weight is [tex]\(x - 7.5\)[/tex].
- The maximum acceptable weight is [tex]\(x + 7.5\)[/tex].
2. Representing the Range Mathematically:
- We can use inequalities to express this range. The actual weight of the suitcase, which we'll call [tex]\(weight\)[/tex], can be between these two calculated limits.
- Thus, the inequalities representing this range are:
- [tex]\(x - 7.5 \leq weight\)[/tex]
- [tex]\(weight \leq x + 7.5\)[/tex]
3. Putting it All Together:
- By combining these expressions, we can say that the suitcase weight is acceptable if it satisfies both inequalities:
- [tex]\(x - 7.5 \leq weight \leq x + 7.5\)[/tex].
This step-by-step explanation provides the framework to understand and determine the acceptable weight range of a suitcase based on the described rule of variation by [tex]\(7.5\)[/tex] units.
