High School

Which number(s) below belong to the solution set of the inequality? Check all that apply.

\[ x + 22 < 32 \]

A. 71
B. 5
C. 8
D. 10
E. 0
F. 15

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.