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Answer :
To solve the inequality [tex]\( x + 10 < 50 \)[/tex] and identify which numbers from the given options belong to the solution set, follow these steps:
1. Rearrange the Inequality:
We start with the inequality:
[tex]\[
x + 10 < 50
\][/tex]
Subtract 10 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x < 40
\][/tex]
This means [tex]\( x \)[/tex] must be less than 40 to satisfy the inequality.
2. Check Each Option:
Now, let's check each number to see if it is less than 40:
- A. 40: Since [tex]\( 40 \not< 40 \)[/tex], 40 does not satisfy the inequality.
- B. 16: Since [tex]\( 16 < 40 \)[/tex], 16 satisfies the inequality.
- C. 84: Since [tex]\( 84 \not< 40 \)[/tex], 84 does not satisfy the inequality.
- D. 50: Since [tex]\( 50 \not< 40 \)[/tex], 50 does not satisfy the inequality.
- E. 39: Since [tex]\( 39 < 40 \)[/tex], 39 satisfies the inequality.
- F. 41: Since [tex]\( 41 \not< 40 \)[/tex], 41 does not satisfy the inequality.
3. Conclusion:
The numbers that satisfy the inequality [tex]\( x < 40 \)[/tex] are 16 and 39. Therefore, the solution set for the inequality is:
[tex]\[
\{16, 39\}
\][/tex]
These are the numbers that belong to the solution set of the inequality [tex]\( x + 10 < 50 \)[/tex].
1. Rearrange the Inequality:
We start with the inequality:
[tex]\[
x + 10 < 50
\][/tex]
Subtract 10 from both sides to solve for [tex]\( x \)[/tex]:
[tex]\[
x < 40
\][/tex]
This means [tex]\( x \)[/tex] must be less than 40 to satisfy the inequality.
2. Check Each Option:
Now, let's check each number to see if it is less than 40:
- A. 40: Since [tex]\( 40 \not< 40 \)[/tex], 40 does not satisfy the inequality.
- B. 16: Since [tex]\( 16 < 40 \)[/tex], 16 satisfies the inequality.
- C. 84: Since [tex]\( 84 \not< 40 \)[/tex], 84 does not satisfy the inequality.
- D. 50: Since [tex]\( 50 \not< 40 \)[/tex], 50 does not satisfy the inequality.
- E. 39: Since [tex]\( 39 < 40 \)[/tex], 39 satisfies the inequality.
- F. 41: Since [tex]\( 41 \not< 40 \)[/tex], 41 does not satisfy the inequality.
3. Conclusion:
The numbers that satisfy the inequality [tex]\( x < 40 \)[/tex] are 16 and 39. Therefore, the solution set for the inequality is:
[tex]\[
\{16, 39\}
\][/tex]
These are the numbers that belong to the solution set of the inequality [tex]\( x + 10 < 50 \)[/tex].
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