High School

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

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

Answer :

To solve the inequality [tex]\( x + 24 < 50 \)[/tex], we want to find the values of [tex]\( x \)[/tex] that make the inequality true. Let's go through the steps to do this:

1. Start with the inequality:
[tex]\[
x + 24 < 50
\][/tex]

2. Subtract 24 from both sides of the inequality to solve for [tex]\( x \)[/tex]:
[tex]\[
x < 50 - 24
\][/tex]

3. Simplify the right side:
[tex]\[
x < 26
\][/tex]

This means that any number less than 26 satisfies the inequality. Now, let's check each of the given numbers to see if they belong to the solution set:

- A. 26: This number is not less than 26, so it does not satisfy [tex]\( x < 26 \)[/tex].
- B. 2: This number is less than 26, so it satisfies the inequality.
- C. 25: This number is less than 26, so it satisfies the inequality.
- D. 74: This number is not less than 26, so it does not satisfy the inequality.
- E. 76: This number is not less than 26, so it does not satisfy the inequality.
- F. 148: This number is not less than 26, so it does not satisfy the inequality.

Therefore, the numbers that satisfy the inequality [tex]\( x + 24 < 50 \)[/tex] are 2 and 25.

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