Answer :
To solve the inequality [tex]\( x + 10 < 50 \)[/tex] and determine which numbers belong to the solution set, let's break it down step by step:
1. Isolate [tex]\( x \)[/tex] in the inequality:
[tex]\[
x + 10 < 50
\][/tex]
To solve for [tex]\( x \)[/tex], subtract 10 from both sides to keep the inequality balanced:
[tex]\[
x < 50 - 10
\][/tex]
[tex]\[
x < 40
\][/tex]
This tells us that any number less than 40 will be a part of the solution set.
2. Check each number against the inequality [tex]\( x < 40 \)[/tex]:
- A. 41: Since 41 is greater than 40, it is not a solution.
- B. 39: Since 39 is less than 40, it is a solution.
- C. 84: Since 84 is greater than 40, it is not a solution.
- D. 16: Since 16 is less than 40, it is a solution.
- E. 50: Since 50 is greater than 40, it is not a solution.
- F. 40: Although 40 equals the cutoff value, we are looking for numbers less than 40, so it is not a solution.
Therefore, the numbers that belong to the solution set are 39 and 16.
1. Isolate [tex]\( x \)[/tex] in the inequality:
[tex]\[
x + 10 < 50
\][/tex]
To solve for [tex]\( x \)[/tex], subtract 10 from both sides to keep the inequality balanced:
[tex]\[
x < 50 - 10
\][/tex]
[tex]\[
x < 40
\][/tex]
This tells us that any number less than 40 will be a part of the solution set.
2. Check each number against the inequality [tex]\( x < 40 \)[/tex]:
- A. 41: Since 41 is greater than 40, it is not a solution.
- B. 39: Since 39 is less than 40, it is a solution.
- C. 84: Since 84 is greater than 40, it is not a solution.
- D. 16: Since 16 is less than 40, it is a solution.
- E. 50: Since 50 is greater than 40, it is not a solution.
- F. 40: Although 40 equals the cutoff value, we are looking for numbers less than 40, so it is not a solution.
Therefore, the numbers that belong to the solution set are 39 and 16.
