High School

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Which number(s) below belong to the solution set of the inequality [tex]x + 24 < 50[/tex]? Check all that apply.

A. 26
B. 2
C. 25
D. 76
E. 148
F. 74

Answer :

Let's solve the inequality step-by-step to find the numbers that belong to its solution set.

We have the inequality:
[tex]\[ x + 24 < 50 \][/tex]

1. Subtract 24 from both sides of the inequality to isolate [tex]\( x \)[/tex]:
[tex]\[ x + 24 - 24 < 50 - 24 \][/tex]
[tex]\[ x < 26 \][/tex]

Now, we know that any number less than 26 is part of the solution set.

2. Check each of the given numbers to see if they are less than 26:

- A. 26:
- 26 is not less than 26, so it does not belong to the solution set.

- B. 2:
- 2 is less than 26, so it belongs to the solution set.

- C. 25:
- 25 is less than 26, so it belongs to the solution set.

- D. 76:
- 76 is not less than 26, so it does not belong to the solution set.

- E. 148:
- 148 is not less than 26, so it does not belong to the solution set.

- F. 74:
- 74 is not less than 26, so it does not belong to the solution set.

Therefore, the numbers that belong to the solution set of the inequality [tex]\( x + 24 < 50 \)[/tex] are B. 2 and C. 25.

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