Answer :
To solve the inequality [tex]\( x + 24 < 50 \)[/tex] and determine which numbers belong to the solution set, follow these steps:
1. Solve the Inequality:
- Start with the inequality: [tex]\( x + 24 < 50 \)[/tex].
- Subtract 24 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x < 50 - 24
\][/tex]
- Calculate the right side:
[tex]\[
x < 26
\][/tex]
- So, the solution set includes all numbers less than 26.
2. Evaluate Each Option:
- A. 2: Check if 2 is less than 26. Yes, 2 < 26.
- B. 26: Check if 26 is less than 26. No, 26 is not less than 26.
- C. 25: Check if 25 is less than 26. Yes, 25 < 26.
- D. 74: Check if 74 is less than 26. No, 74 is greater.
- E. 76: Check if 76 is less than 26. No, 76 is greater.
- F. 148: Check if 148 is less than 26. No, 148 is greater.
3. Determine the Solution Set:
- The numbers that satisfy the inequality [tex]\( x < 26 \)[/tex] are 2 and 25.
Therefore, the solution set includes options A (2) and C (25).
1. Solve the Inequality:
- Start with the inequality: [tex]\( x + 24 < 50 \)[/tex].
- Subtract 24 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x < 50 - 24
\][/tex]
- Calculate the right side:
[tex]\[
x < 26
\][/tex]
- So, the solution set includes all numbers less than 26.
2. Evaluate Each Option:
- A. 2: Check if 2 is less than 26. Yes, 2 < 26.
- B. 26: Check if 26 is less than 26. No, 26 is not less than 26.
- C. 25: Check if 25 is less than 26. Yes, 25 < 26.
- D. 74: Check if 74 is less than 26. No, 74 is greater.
- E. 76: Check if 76 is less than 26. No, 76 is greater.
- F. 148: Check if 148 is less than 26. No, 148 is greater.
3. Determine the Solution Set:
- The numbers that satisfy the inequality [tex]\( x < 26 \)[/tex] are 2 and 25.
Therefore, the solution set includes options A (2) and C (25).
