To determine which number(s) belong to the solution set of the equation [tex]\( 22x = 902 \)[/tex], we need to perform the following steps:
1. Solve for [tex]\( x \)[/tex] in the given equation:
The equation is [tex]\( 22x = 902 \)[/tex].
To isolate [tex]\( x \)[/tex], divide both sides of the equation by 22:
[tex]\[
x = \frac{902}{22}
\][/tex]
2. Calculate [tex]\( x \)[/tex]:
Simplifying the right side:
[tex]\[
x = \frac{902}{22} = 41
\][/tex]
Thus, [tex]\( x = 41 \)[/tex].
3. Check each number from the given list to see if it satisfies the equation [tex]\( 22x = 902 \)[/tex]:
- Option A: 44
[tex]\[
22 \times 44 = 968 \quad (\text{not } 902)
\][/tex]
So, 44 does not belong to the solution set.
- Option B: 63
[tex]\[
22 \times 63 = 1386 \quad (\text{not } 902)
\][/tex]
So, 63 does not belong to the solution set.
- Option C: 19
[tex]\[
22 \times 19 = 418 \quad (\text{not } 902)
\][/tex]
So, 19 does not belong to the solution set.
- Option D: 902
[tex]\[
22 \times 902 = 19844 \quad (\text{not } 902)
\][/tex]
So, 902 does not belong to the solution set.
- Option E: 82
[tex]\[
22 \times 82 = 1804 \quad (\text{not } 902)
\][/tex]
So, 82 does not belong to the solution set.
- Option F: 41
[tex]\[
22 \times 41 = 902 \quad (\text{exactly correct})
\][/tex]
So, 41 belongs to the solution set.
Therefore, only the number 41 belongs to the solution set of the equation [tex]\( 22x = 902 \)[/tex].
