Answer :
To solve the inequality [tex]\( x + 6 < 38 \)[/tex], we need to find the values of [tex]\( x \)[/tex] that make this true. Let's go through the steps:
1. Start with the inequality:
[tex]\[
x + 6 < 38
\][/tex]
2. Isolate [tex]\( x \)[/tex] by subtracting 6 from both sides:
[tex]\[
x + 6 - 6 < 38 - 6
\][/tex]
[tex]\[
x < 32
\][/tex]
Now we know that [tex]\( x \)[/tex] must be less than 32. Let's check which numbers from the options are less than 32:
- Option A: 32
- [tex]\( 32 \not< 32 \)[/tex] (32 is not less than 32)
- Option B: 26
- [tex]\( 26 < 32 \)[/tex] (26 is less than 32)
- Option C: 88
- [tex]\( 88 \not< 32 \)[/tex] (88 is not less than 32)
- Option D: 70
- [tex]\( 70 \not< 32 \)[/tex] (70 is not less than 32)
- Option E: 44
- [tex]\( 44 \not< 32 \)[/tex] (44 is not less than 32)
- Option F: 31
- [tex]\( 31 < 32 \)[/tex] (31 is less than 32)
Therefore, the numbers that belong to the solution set of the inequality [tex]\( x + 6 < 38 \)[/tex] are 26 and 31.
1. Start with the inequality:
[tex]\[
x + 6 < 38
\][/tex]
2. Isolate [tex]\( x \)[/tex] by subtracting 6 from both sides:
[tex]\[
x + 6 - 6 < 38 - 6
\][/tex]
[tex]\[
x < 32
\][/tex]
Now we know that [tex]\( x \)[/tex] must be less than 32. Let's check which numbers from the options are less than 32:
- Option A: 32
- [tex]\( 32 \not< 32 \)[/tex] (32 is not less than 32)
- Option B: 26
- [tex]\( 26 < 32 \)[/tex] (26 is less than 32)
- Option C: 88
- [tex]\( 88 \not< 32 \)[/tex] (88 is not less than 32)
- Option D: 70
- [tex]\( 70 \not< 32 \)[/tex] (70 is not less than 32)
- Option E: 44
- [tex]\( 44 \not< 32 \)[/tex] (44 is not less than 32)
- Option F: 31
- [tex]\( 31 < 32 \)[/tex] (31 is less than 32)
Therefore, the numbers that belong to the solution set of the inequality [tex]\( x + 6 < 38 \)[/tex] are 26 and 31.
