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Answer :
To determine which inequality describes the scenario where the weight limit for a bridge is 10,000 pounds, let's break down the information:
1. Understanding the Weight Limit: The bridge can safely hold up to a maximum of 10,000 pounds. This means that any weight on the bridge must not exceed this limit.
2. Choosing the Correct Inequality:
- We need an inequality that indicates the weight, denoted as [tex]\( w \)[/tex], can be at most 10,000 pounds.
- This means [tex]\( w \)[/tex] can be exactly 10,000 pounds or any amount less than that.
3. Analyzing the Inequality Options:
- [tex]\( a. \, w \leq 10000 \)[/tex]: This means the weight can be less than or exactly 10,000 pounds, which fits the description of the weight limit perfectly.
- [tex]\( b. \, w \geq 10000 \)[/tex]: This means the weight must be 10,000 pounds or more, which does not fit because the bridge cannot hold more than 10,000 pounds.
- [tex]\( c. \, w < 10000 \)[/tex]: This means the weight must be less than 10,000 pounds and does not allow for a weight of exactly 10,000 pounds, which would also be acceptable.
- [tex]\( d. \, w > 10000 \)[/tex]: This means the weight must be more than 10,000 pounds, which is incorrect because it exceeds the weight limit.
4. Conclusion:
- The inequality that best describes the weight limit for the bridge is [tex]\( w \leq 10000 \)[/tex].
Thus, the correct answer is option a: [tex]\( w \leq 10000 \)[/tex]. This inequality captures the requirement that the weight on the bridge must be at most 10,000 pounds.
1. Understanding the Weight Limit: The bridge can safely hold up to a maximum of 10,000 pounds. This means that any weight on the bridge must not exceed this limit.
2. Choosing the Correct Inequality:
- We need an inequality that indicates the weight, denoted as [tex]\( w \)[/tex], can be at most 10,000 pounds.
- This means [tex]\( w \)[/tex] can be exactly 10,000 pounds or any amount less than that.
3. Analyzing the Inequality Options:
- [tex]\( a. \, w \leq 10000 \)[/tex]: This means the weight can be less than or exactly 10,000 pounds, which fits the description of the weight limit perfectly.
- [tex]\( b. \, w \geq 10000 \)[/tex]: This means the weight must be 10,000 pounds or more, which does not fit because the bridge cannot hold more than 10,000 pounds.
- [tex]\( c. \, w < 10000 \)[/tex]: This means the weight must be less than 10,000 pounds and does not allow for a weight of exactly 10,000 pounds, which would also be acceptable.
- [tex]\( d. \, w > 10000 \)[/tex]: This means the weight must be more than 10,000 pounds, which is incorrect because it exceeds the weight limit.
4. Conclusion:
- The inequality that best describes the weight limit for the bridge is [tex]\( w \leq 10000 \)[/tex].
Thus, the correct answer is option a: [tex]\( w \leq 10000 \)[/tex]. This inequality captures the requirement that the weight on the bridge must be at most 10,000 pounds.
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