First, let us denote the values given in the problem:
- [tex]\( x = 8 \)[/tex]
- [tex]\( y = 4 \)[/tex]
- [tex]\( a = 6 \)[/tex]
- We are given multiple choices for [tex]\( b + x \)[/tex]: 14, 12, 18, 16
To find the values of [tex]\( b \)[/tex] corresponding to each possible value of [tex]\( b + x \)[/tex], we start with each option and subtract [tex]\( x \)[/tex] from it.
1. For [tex]\( b + x = 14 \)[/tex]:
[tex]\[
b + 8 = 14 \implies b = 14 - 8 = 6
\][/tex]
2. For [tex]\( b + x = 12 \)[/tex]:
[tex]\[
b + 8 = 12 \implies b = 12 - 8 = 4
\][/tex]
3. For [tex]\( b + x = 18 \)[/tex]:
[tex]\[
b + 8 = 18 \implies b = 18 - 8 = 10
\][/tex]
4. For [tex]\( b + x = 16 \)[/tex]:
[tex]\[
b + 8 = 16 \implies b = 16 - 8 = 8
\][/tex]
Thus, we have calculated the possible values of [tex]\( b \)[/tex]:
[tex]\[
b \in \{6, 4, 10, 8\}
\][/tex]
So based on our given problem, the possible values for [tex]\( b \)[/tex] are 6, 4, 10, and 8.
