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Answer :
To find which numbers belong to the solution set of the inequality [tex]\(x + 22 < 32\)[/tex], we need to solve this inequality step by step.
1. Solve the Inequality:
- Start with the inequality [tex]\(x + 22 < 32\)[/tex].
- To isolate [tex]\(x\)[/tex], subtract 22 from both sides of the inequality:
[tex]\[
x + 22 - 22 < 32 - 22
\][/tex]
- This simplifies to:
[tex]\[
x < 10
\][/tex]
This means that [tex]\(x\)[/tex] must be less than 10.
2. Check Each Number:
- We now need to check which of the given numbers are less than 10:
- A. 8: Since [tex]\(8 < 10\)[/tex], this number belongs to the solution set.
- B. 5: Since [tex]\(5 < 10\)[/tex], this number belongs to the solution set.
- C. 15: Since [tex]\(15\)[/tex] is not less than 10, it does not belong to the solution set.
- D. 71: Since [tex]\(71\)[/tex] is not less than 10, it does not belong to the solution set.
- E. 0: Since [tex]\(0 < 10\)[/tex], this number belongs to the solution set.
- F. 10: Since [tex]\(10\)[/tex] is not less than 10 (it's exactly 10), it does not belong to the solution set.
3. Conclusion:
- The numbers that satisfy the inequality [tex]\(x < 10\)[/tex] and thus belong to the solution set are: 8, 5, and 0.
So, the numbers that belong to the solution set of the inequality are A (8), B (5), and E (0).
1. Solve the Inequality:
- Start with the inequality [tex]\(x + 22 < 32\)[/tex].
- To isolate [tex]\(x\)[/tex], subtract 22 from both sides of the inequality:
[tex]\[
x + 22 - 22 < 32 - 22
\][/tex]
- This simplifies to:
[tex]\[
x < 10
\][/tex]
This means that [tex]\(x\)[/tex] must be less than 10.
2. Check Each Number:
- We now need to check which of the given numbers are less than 10:
- A. 8: Since [tex]\(8 < 10\)[/tex], this number belongs to the solution set.
- B. 5: Since [tex]\(5 < 10\)[/tex], this number belongs to the solution set.
- C. 15: Since [tex]\(15\)[/tex] is not less than 10, it does not belong to the solution set.
- D. 71: Since [tex]\(71\)[/tex] is not less than 10, it does not belong to the solution set.
- E. 0: Since [tex]\(0 < 10\)[/tex], this number belongs to the solution set.
- F. 10: Since [tex]\(10\)[/tex] is not less than 10 (it's exactly 10), it does not belong to the solution set.
3. Conclusion:
- The numbers that satisfy the inequality [tex]\(x < 10\)[/tex] and thus belong to the solution set are: 8, 5, and 0.
So, the numbers that belong to the solution set of the inequality are A (8), B (5), and E (0).
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