Answer :
To solve the inequality [tex]\( x + 22 < 32 \)[/tex], we need to find the values of [tex]\( x \)[/tex] that make this inequality true. Here's a step-by-step explanation:
1. Subtract 22 from both sides of the inequality:
Start with the inequality:
[tex]\( x + 22 < 32 \)[/tex]
Subtract 22 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\( x + 22 - 22 < 32 - 22 \)[/tex]
Simplify:
[tex]\( x < 10 \)[/tex]
2. Identify numbers less than 10:
We'll test each option to see if it's less than 10, which will determine if it belongs to the solution set of the inequality:
- A. 71 (Not less than 10)
- B. 5 (Less than 10)
- C. 8 (Less than 10)
- D. 10 (Not less than 10, because 10 is not included in "less than 10")
- E. 0 (Less than 10)
- F. 15 (Not less than 10)
3. Conclusion:
Based on the inequality [tex]\( x < 10 \)[/tex], the numbers that belong to the solution set from the options provided are 5, 8, and 0.
1. Subtract 22 from both sides of the inequality:
Start with the inequality:
[tex]\( x + 22 < 32 \)[/tex]
Subtract 22 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\( x + 22 - 22 < 32 - 22 \)[/tex]
Simplify:
[tex]\( x < 10 \)[/tex]
2. Identify numbers less than 10:
We'll test each option to see if it's less than 10, which will determine if it belongs to the solution set of the inequality:
- A. 71 (Not less than 10)
- B. 5 (Less than 10)
- C. 8 (Less than 10)
- D. 10 (Not less than 10, because 10 is not included in "less than 10")
- E. 0 (Less than 10)
- F. 15 (Not less than 10)
3. Conclusion:
Based on the inequality [tex]\( x < 10 \)[/tex], the numbers that belong to the solution set from the options provided are 5, 8, and 0.
