Discussion

If x = k, is the solution of the equation :

\[ \frac{x - 4}{7} - 1 = \frac{5 - x}{3} + x \]

then what is the value of \(\dfrac{11k + 18}{11k - 12}\) ?

Answer: D

The value is \(\frac{5}{8}\).

Multiply the equation by 21 to clear the fractions:

\[ \begin{aligned} 3(x - 4) - 21 &= 7(5 - x) + 21x \\ 3x - 33 &= 35 + 14x \\ -11x &= 68 \end{aligned} \]

So 11k = -68, and

\[ \begin{aligned} \frac{11k + 18}{11k - 12} &= \frac{-68 + 18}{-68 - 12} \\ &= \frac{-50}{-80} = \frac{5}{8} \end{aligned} \]

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