IDNLearn.com connects you with a community of knowledgeable individuals ready to help. Ask your questions and get detailed, reliable answers from our community of experienced experts.
Sagot :
Sure, let's solve the problem step by step.
We have a compound inequality:
[tex]\[ 10 < x < 20 \][/tex]
This means we are looking for numbers that satisfy:
- Greater than 10
- Less than 20
Let's check each set of numbers to see which numbers satisfy the compound inequality [tex]\( 10 < x < 20 \)[/tex].
1. For the set [tex]\(\{-7, 5, 18, 24, 32\}\)[/tex]:
- [tex]\(-7\)[/tex] is not greater than 10.
- [tex]\(5\)[/tex] is not greater than 10.
- [tex]\(18\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(24\)[/tex] is not less than 20.
- [tex]\(32\)[/tex] is not less than 20.
So, the only number in this set that satisfies the inequality is [tex]\(18\)[/tex]. Therefore, [tex]\(\{18\}\)[/tex].
The count of numbers satisfying the inequality: 1.
2. For the set [tex]\(\{-9, 7, 15, 22, 26\}\)[/tex]:
- [tex]\(-9\)[/tex] is not greater than 10.
- [tex]\(7\)[/tex] is not greater than 10.
- [tex]\(15\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(22\)[/tex] is not less than 20.
- [tex]\(26\)[/tex] is not less than 20.
So, the only number in this set that satisfies the inequality is [tex]\(15\)[/tex]. Therefore, [tex]\(\{15\}\)[/tex].
The count of numbers satisfying the inequality: 1.
3. For the set [tex]\(\{16, 17, 22, 23, 24\}\)[/tex]:
- [tex]\(16\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(17\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(22\)[/tex] is not less than 20.
- [tex]\(23\)[/tex] is not less than 20.
- [tex]\(24\)[/tex] is not less than 20.
So, the numbers in this set that satisfy the inequality are [tex]\(16\)[/tex] and [tex]\(17\)[/tex]. Therefore, [tex]\(\{16, 17\}\)[/tex].
The count of numbers satisfying the inequality: 2.
4. For the set [tex]\(\{18, 19, 20, 21, 22\}\)[/tex]:
- [tex]\(18\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(19\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(20\)[/tex] is not less than 20.
- [tex]\(21\)[/tex] is not less than 20.
- [tex]\(22\)[/tex] is not less than 20.
So, the numbers in this set that satisfy the inequality are [tex]\(18\)[/tex] and [tex]\(19\)[/tex]. Therefore, [tex]\(\{18, 19\}\)[/tex].
The count of numbers satisfying the inequality: 2.
Summarizing the results:
- For set [tex]\(\{-7, 5, 18, 24, 32\}\)[/tex]: 1 number (18)
- For set [tex]\(\{-9, 7, 15, 22, 26\}\)[/tex]: 1 number (15)
- For set [tex]\(\{16, 17, 22, 23, 24\}\)[/tex]: 2 numbers (16, 17)
- For set [tex]\(\{18, 19, 20, 21, 22\}\)[/tex]: 2 numbers (18, 19)
Sets with the maximum numbers satisfying the inequality are:
[tex]\(\{16, 17, 22, 23, 24\}\)[/tex] and [tex]\(\{18, 19, 20, 21, 22\}\)[/tex] each with 2 numbers within the range [tex]\( 10 < x < 20 \)[/tex].
We have a compound inequality:
[tex]\[ 10 < x < 20 \][/tex]
This means we are looking for numbers that satisfy:
- Greater than 10
- Less than 20
Let's check each set of numbers to see which numbers satisfy the compound inequality [tex]\( 10 < x < 20 \)[/tex].
1. For the set [tex]\(\{-7, 5, 18, 24, 32\}\)[/tex]:
- [tex]\(-7\)[/tex] is not greater than 10.
- [tex]\(5\)[/tex] is not greater than 10.
- [tex]\(18\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(24\)[/tex] is not less than 20.
- [tex]\(32\)[/tex] is not less than 20.
So, the only number in this set that satisfies the inequality is [tex]\(18\)[/tex]. Therefore, [tex]\(\{18\}\)[/tex].
The count of numbers satisfying the inequality: 1.
2. For the set [tex]\(\{-9, 7, 15, 22, 26\}\)[/tex]:
- [tex]\(-9\)[/tex] is not greater than 10.
- [tex]\(7\)[/tex] is not greater than 10.
- [tex]\(15\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(22\)[/tex] is not less than 20.
- [tex]\(26\)[/tex] is not less than 20.
So, the only number in this set that satisfies the inequality is [tex]\(15\)[/tex]. Therefore, [tex]\(\{15\}\)[/tex].
The count of numbers satisfying the inequality: 1.
3. For the set [tex]\(\{16, 17, 22, 23, 24\}\)[/tex]:
- [tex]\(16\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(17\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(22\)[/tex] is not less than 20.
- [tex]\(23\)[/tex] is not less than 20.
- [tex]\(24\)[/tex] is not less than 20.
So, the numbers in this set that satisfy the inequality are [tex]\(16\)[/tex] and [tex]\(17\)[/tex]. Therefore, [tex]\(\{16, 17\}\)[/tex].
The count of numbers satisfying the inequality: 2.
4. For the set [tex]\(\{18, 19, 20, 21, 22\}\)[/tex]:
- [tex]\(18\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(19\)[/tex] is greater than 10 and less than 20. ✓
- [tex]\(20\)[/tex] is not less than 20.
- [tex]\(21\)[/tex] is not less than 20.
- [tex]\(22\)[/tex] is not less than 20.
So, the numbers in this set that satisfy the inequality are [tex]\(18\)[/tex] and [tex]\(19\)[/tex]. Therefore, [tex]\(\{18, 19\}\)[/tex].
The count of numbers satisfying the inequality: 2.
Summarizing the results:
- For set [tex]\(\{-7, 5, 18, 24, 32\}\)[/tex]: 1 number (18)
- For set [tex]\(\{-9, 7, 15, 22, 26\}\)[/tex]: 1 number (15)
- For set [tex]\(\{16, 17, 22, 23, 24\}\)[/tex]: 2 numbers (16, 17)
- For set [tex]\(\{18, 19, 20, 21, 22\}\)[/tex]: 2 numbers (18, 19)
Sets with the maximum numbers satisfying the inequality are:
[tex]\(\{16, 17, 22, 23, 24\}\)[/tex] and [tex]\(\{18, 19, 20, 21, 22\}\)[/tex] each with 2 numbers within the range [tex]\( 10 < x < 20 \)[/tex].
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.
