Answer :
To solve the inequality [tex]\(x \leq 82\)[/tex], we need to determine which values of [tex]\(x\)[/tex] satisfy this condition. We're given a set of possible answers, and we have to check each set to see if all its values satisfy the inequality.
Let's go through each option step-by-step:
Option A: 82, 81.5, 0, and -4
- Check if 82 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 82 is equal to 82.
- Check if 81.5 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 81.5 is less than 82.
- Check if 0 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 0 is less than 82.
- Check if -4 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because -4 is less than 82.
All numbers in Option A satisfy the inequality.
Option B: 82, 85, 95.5, and 100
- Check if 82 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 82 is equal to 82.
- Check if 85 satisfies [tex]\(x \leq 82\)[/tex]: No, because 85 is greater than 82.
- Check if 95.5 satisfies [tex]\(x \leq 82\)[/tex]: No, because 95.5 is greater than 82.
- Check if 100 satisfies [tex]\(x \leq 82\)[/tex]: No, because 100 is greater than 82.
Not all numbers in Option B satisfy the inequality.
Option C: 82.5, 12, 10.5, and 0
- Check if 82.5 satisfies [tex]\(x \leq 82\)[/tex]: No, because 82.5 is greater than 82.
- Check if 12 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 12 is less than 82.
- Check if 10.5 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 10.5 is less than 82.
- Check if 0 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 0 is less than 82.
Not all numbers in Option C satisfy the inequality.
Option D: 82.5, 87, 90, and 100
- Check if 82.5 satisfies [tex]\(x \leq 82\)[/tex]: No, because 82.5 is greater than 82.
- Check if 87 satisfies [tex]\(x \leq 82\)[/tex]: No, because 87 is greater than 82.
- Check if 90 satisfies [tex]\(x \leq 82\)[/tex]: No, because 90 is greater than 82.
- Check if 100 satisfies [tex]\(x \leq 82\)[/tex]: No, because 100 is greater than 82.
All numbers in Option D are greater than 82 and do not satisfy the inequality.
Therefore, after evaluating each option, we find that Option A (82, 81.5, 0, and -4) contains values that all satisfy the inequality [tex]\(x \leq 82\)[/tex]. So, the correct answer is Option A.
Let's go through each option step-by-step:
Option A: 82, 81.5, 0, and -4
- Check if 82 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 82 is equal to 82.
- Check if 81.5 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 81.5 is less than 82.
- Check if 0 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 0 is less than 82.
- Check if -4 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because -4 is less than 82.
All numbers in Option A satisfy the inequality.
Option B: 82, 85, 95.5, and 100
- Check if 82 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 82 is equal to 82.
- Check if 85 satisfies [tex]\(x \leq 82\)[/tex]: No, because 85 is greater than 82.
- Check if 95.5 satisfies [tex]\(x \leq 82\)[/tex]: No, because 95.5 is greater than 82.
- Check if 100 satisfies [tex]\(x \leq 82\)[/tex]: No, because 100 is greater than 82.
Not all numbers in Option B satisfy the inequality.
Option C: 82.5, 12, 10.5, and 0
- Check if 82.5 satisfies [tex]\(x \leq 82\)[/tex]: No, because 82.5 is greater than 82.
- Check if 12 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 12 is less than 82.
- Check if 10.5 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 10.5 is less than 82.
- Check if 0 satisfies [tex]\(x \leq 82\)[/tex]: Yes, because 0 is less than 82.
Not all numbers in Option C satisfy the inequality.
Option D: 82.5, 87, 90, and 100
- Check if 82.5 satisfies [tex]\(x \leq 82\)[/tex]: No, because 82.5 is greater than 82.
- Check if 87 satisfies [tex]\(x \leq 82\)[/tex]: No, because 87 is greater than 82.
- Check if 90 satisfies [tex]\(x \leq 82\)[/tex]: No, because 90 is greater than 82.
- Check if 100 satisfies [tex]\(x \leq 82\)[/tex]: No, because 100 is greater than 82.
All numbers in Option D are greater than 82 and do not satisfy the inequality.
Therefore, after evaluating each option, we find that Option A (82, 81.5, 0, and -4) contains values that all satisfy the inequality [tex]\(x \leq 82\)[/tex]. So, the correct answer is Option A.
