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Which number(s) below belong to the solution set of the inequality [tex]\( x + 22 \ \textless \ 32 \)[/tex]? Check all that apply.

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

Answer :

To solve the inequality [tex]\(x + 22 < 32\)[/tex], follow these steps:

1. Isolate [tex]\(x\)[/tex]: Begin by subtracting 22 from both sides of the inequality to isolate [tex]\(x\)[/tex].
[tex]\[
x + 22 - 22 < 32 - 22
\][/tex]
Simplifying both sides gives:
[tex]\[
x < 10
\][/tex]

2. Determine the solution set: Next, we need to identify which numbers from the given options satisfy the inequality [tex]\(x < 10\)[/tex].

- Option A: 5
[tex]\[
5 < 10 \quad \text{(True)}
\][/tex]

- Option B: 15
[tex]\[
15 < 10 \quad \text{(False)}
\][/tex]

- Option C: 71
[tex]\[
71 < 10 \quad \text{(False)}
\][/tex]

- Option D: 0
[tex]\[
0 < 10 \quad \text{(True)}
\][/tex]

- Option E: 8
[tex]\[
8 < 10 \quad \text{(True)}
\][/tex]

- Option F: 10
[tex]\[
10 < 10 \quad \text{(False)}
\][/tex]

3. Conclusion: The numbers that satisfy the condition [tex]\(x < 10\)[/tex] are 5, 0, and 8. Therefore, the correct choices are:

- A. 5
- D. 0
- E. 8

These are the numbers that belong to the solution set of the inequality [tex]\(x + 22 < 32\)[/tex].

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