Answer :
Sure! Let's solve the inequality [tex]\(x + 6 < 38\)[/tex] step-by-step to find which numbers belong to the solution set.
1. Simplify the Inequality:
- Start with the inequality: [tex]\(x + 6 < 38\)[/tex].
- To isolate [tex]\(x\)[/tex], subtract 6 from both sides:
[tex]\[
x + 6 - 6 < 38 - 6
\][/tex]
- This simplifies to:
[tex]\[
x < 32
\][/tex]
- So, [tex]\(x\)[/tex] must be less than 32.
2. Check Each Number:
We need to check each given number to see if it is less than 32.
- A. 31: Since 31 is less than 32, it satisfies the inequality.
- B. 70: 70 is greater than 32, so it does not satisfy the inequality.
- C. 44: 44 is greater than 32, so it does not satisfy the inequality.
- D. 32: 32 is equal to 32, but it needs to be less than 32, so it does not satisfy the inequality.
- E. 26: Since 26 is less than 32, it satisfies the inequality.
- F. 88: 88 is greater than 32, so it does not satisfy the inequality.
3. Conclusion:
The numbers that satisfy the inequality [tex]\(x < 32\)[/tex] are 31 and 26.
Therefore, the numbers that belong to the solution set of the inequality are:
- 31
- 26
1. Simplify the Inequality:
- Start with the inequality: [tex]\(x + 6 < 38\)[/tex].
- To isolate [tex]\(x\)[/tex], subtract 6 from both sides:
[tex]\[
x + 6 - 6 < 38 - 6
\][/tex]
- This simplifies to:
[tex]\[
x < 32
\][/tex]
- So, [tex]\(x\)[/tex] must be less than 32.
2. Check Each Number:
We need to check each given number to see if it is less than 32.
- A. 31: Since 31 is less than 32, it satisfies the inequality.
- B. 70: 70 is greater than 32, so it does not satisfy the inequality.
- C. 44: 44 is greater than 32, so it does not satisfy the inequality.
- D. 32: 32 is equal to 32, but it needs to be less than 32, so it does not satisfy the inequality.
- E. 26: Since 26 is less than 32, it satisfies the inequality.
- F. 88: 88 is greater than 32, so it does not satisfy the inequality.
3. Conclusion:
The numbers that satisfy the inequality [tex]\(x < 32\)[/tex] are 31 and 26.
Therefore, the numbers that belong to the solution set of the inequality are:
- 31
- 26
