Discussion
The solution of the equation \(\dfrac{(x + 1) - (2x + 4)}{3 - 5x} = \dfrac{1}{23}\) is also the solution of the equation :
Answer: C
The equation with the same solution is 3 (2x + 3) = 5 (x + 1).
Solve the given equation by cross-multiplying:
\[ \begin{aligned} 23(-x - 3) &= 3 - 5x \\ -23x - 69 &= 3 - 5x \\ -18x &= 72 \Rightarrow x = -4 \end{aligned} \]
Substitute x = -4 in each option: 3(-8 + 3) = -15 and 5(-4 + 1) = -15, so option 3 holds. The others fail: 5(-7) = -35 against 3(-3) = -9; 3(-5) = -15 against 2(-1) = -2; and 2(-11) = -22 against 3(-3) = -9.
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