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

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

Answer :

To solve the inequality [tex]\( x + 22 < 32 \)[/tex], we need to find the values for [tex]\( x \)[/tex] that make this statement true.

Let's go through the steps to solve it:

1. Subtract 22 from both sides of the inequality:
[tex]\[
x + 22 - 22 < 32 - 22
\][/tex]
[tex]\[
x < 10
\][/tex]

The inequality [tex]\( x < 10 \)[/tex] tells us that [tex]\( x \)[/tex] must be a number less than 10.

Now, let's check which given numbers satisfy this inequality. The numbers to consider are:

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

We need to check each number to see if it is less than 10:

- 15 is not less than 10.
- 0 is less than 10.
- 10 is not less than 10 (it is equal to 10).
- 8 is less than 10.
- 71 is not less than 10.
- 5 is less than 10.

The numbers that satisfy the inequality [tex]\( x < 10 \)[/tex] are 0, 8, and 5.

So, the solution set consists of the numbers:

- B. 0
- D. 8
- F. 5

These are the numbers that belong to the solution set of the inequality.

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