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Answer :
To solve the question, we need to express the range of weights allowed for a wrestler to participate in the 145lb weight class as a compound inequality.
1. Understand the Problem:
- The wrestler must weigh within a certain range to qualify for the 145lb weight class.
- The allowed weight range is from 132.1 pounds to 145.0 pounds.
2. Define the Range:
- The lower bound of the range is 132.1 pounds.
- The upper bound of the range is 145.0 pounds.
- Both bounds are inclusive, meaning the wrestler's weight can be exactly 132.1 pounds or exactly 145.0 pounds, and they will still qualify.
3. Write the Compound Inequality:
- A compound inequality is used to represent conditions where one variable is bounded by two values.
- For this problem, the inequality for the weight [tex]\( w \)[/tex] is written as:
[tex]\[
132.1 \leq w \leq 145.0
\][/tex]
- This inequality shows that the wrestler's weight [tex]\( w \)[/tex] must be greater than or equal to 132.1 pounds and less than or equal to 145.0 pounds.
By following these steps, we have written a compound inequality representing the allowed weights for a wrestler in the 145lb weight class.
1. Understand the Problem:
- The wrestler must weigh within a certain range to qualify for the 145lb weight class.
- The allowed weight range is from 132.1 pounds to 145.0 pounds.
2. Define the Range:
- The lower bound of the range is 132.1 pounds.
- The upper bound of the range is 145.0 pounds.
- Both bounds are inclusive, meaning the wrestler's weight can be exactly 132.1 pounds or exactly 145.0 pounds, and they will still qualify.
3. Write the Compound Inequality:
- A compound inequality is used to represent conditions where one variable is bounded by two values.
- For this problem, the inequality for the weight [tex]\( w \)[/tex] is written as:
[tex]\[
132.1 \leq w \leq 145.0
\][/tex]
- This inequality shows that the wrestler's weight [tex]\( w \)[/tex] must be greater than or equal to 132.1 pounds and less than or equal to 145.0 pounds.
By following these steps, we have written a compound inequality representing the allowed weights for a wrestler in the 145lb weight class.
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