Answer :
To solve the inequality [tex]\( x + 6 < 38 \)[/tex], we'll need to find which values of [tex]\( x \)[/tex] make this true.
1. Subtract 6 from both sides: This will help us isolate [tex]\( x \)[/tex] on one side of the inequality.
[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 to see if it satisfies the inequality: We will compare the numbers provided to see if they are less than 32.
- A. 88: Since 88 is greater than 32, it does not satisfy the inequality.
- B. 32: Since 32 is not less than 32 (it's equal), it does not satisfy the inequality.
- C. 70: Since 70 is greater than 32, it does not satisfy the inequality.
- D. 26: Since 26 is less than 32, it satisfies the inequality.
- E. 44: Since 44 is greater than 32, it does not satisfy the inequality.
- F. 31: Since 31 is less than 32, it satisfies the inequality.
The numbers that belong to the solution set of the inequality [tex]\( x + 6 < 38 \)[/tex] are 26 and 31.
1. Subtract 6 from both sides: This will help us isolate [tex]\( x \)[/tex] on one side of the inequality.
[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 to see if it satisfies the inequality: We will compare the numbers provided to see if they are less than 32.
- A. 88: Since 88 is greater than 32, it does not satisfy the inequality.
- B. 32: Since 32 is not less than 32 (it's equal), it does not satisfy the inequality.
- C. 70: Since 70 is greater than 32, it does not satisfy the inequality.
- D. 26: Since 26 is less than 32, it satisfies the inequality.
- E. 44: Since 44 is greater than 32, it does not satisfy the inequality.
- F. 31: Since 31 is less than 32, it satisfies the inequality.
The numbers that belong to the solution set of the inequality [tex]\( x + 6 < 38 \)[/tex] are 26 and 31.
