a) \(\dfrac{8 \cdot 3 + 2 \cdot 8}{10} = \dfrac{24 + 16}{10} = \dfrac{40}{10} = \boxed{4}\)
b) \(\dfrac{8 \cdot 3 + 3 \cdot 8}{11} = \dfrac{24 + 24}{11} = \boxed{\dfrac{48}{11}}\)
c) \(\dfrac{8 \cdot 3 + 4 \cdot 8}{12} = \dfrac{24 + 32}{12} = \dfrac{56}{44} = \boxed{\dfrac{14}{11}}\)
d) \(\begin{align*} \dfrac{8 \cdot 3 + (2 + x) \cdot 8}{10 + x} &= 6 \\ \dfrac{24 + 16 + 8x}{10 + x} &= 6 \\ \dfrac{40 + 8x}{10 + x} &= 6 \\ 40 + 8x &= 60 + 6x \\ 40 + 2x &= 60 \\ 2x &= 20 \\ x &= \boxed{10} \end{align*}\)
e) \(\begin{align*} \dfrac{8 \cdot 3 + (2 + x) \cdot 8}{10 + x} &= 7 \\ \dfrac{24 + 16 + 8x}{10 + x} &= 7 \\ \dfrac{40 + 8x}{10 + x} &= 7 \\ 40 + 8x &= 70 + 7x \\ 40 + x &= 70 \\ x &= \boxed{30} \end{align*}\)
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