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Answer :
To find the negation of the inequality [tex]\( x > 82 \)[/tex], let's break it down step-by-step:
1. Understanding the Original Inequality:
The original inequality [tex]\( x > 82 \)[/tex] means "x is greater than 82." For example, values like 83, 84, or any number greater than 82 would satisfy this inequality.
2. Negation Concept:
Negating an inequality means finding the range of values that do not satisfy the original inequality. Therefore, the negation will include all the values that are not greater than 82.
3. Translation to Inequality Symbols:
If [tex]\( x \)[/tex] is not greater than 82, then [tex]\( x \)[/tex] must either be less than or equal to 82. In inequality terms, this is written as [tex]\( x \leq 82 \)[/tex].
4. Final Answer:
Therefore, the correct negation of the inequality [tex]\( x > 82 \)[/tex] is [tex]\( x \leq 82 \)[/tex].
Given these steps, the answer to the question is option A: [tex]\( x \leq 82 \)[/tex].
1. Understanding the Original Inequality:
The original inequality [tex]\( x > 82 \)[/tex] means "x is greater than 82." For example, values like 83, 84, or any number greater than 82 would satisfy this inequality.
2. Negation Concept:
Negating an inequality means finding the range of values that do not satisfy the original inequality. Therefore, the negation will include all the values that are not greater than 82.
3. Translation to Inequality Symbols:
If [tex]\( x \)[/tex] is not greater than 82, then [tex]\( x \)[/tex] must either be less than or equal to 82. In inequality terms, this is written as [tex]\( x \leq 82 \)[/tex].
4. Final Answer:
Therefore, the correct negation of the inequality [tex]\( x > 82 \)[/tex] is [tex]\( x \leq 82 \)[/tex].
Given these steps, the answer to the question is option A: [tex]\( x \leq 82 \)[/tex].
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