Discussion
If \(\dfrac{5 - 7x}{8 + 3x} = -\dfrac{40}{7}\), then what is the value of \(\dfrac{2x + 3}{x + 9}\) ?
Answer: A
The value is \(-\dfrac{7}{4}\).
First find \(x\) by cross-multiplying:
\[ \begin{aligned} 7(5 - 7x) &= -40(8 + 3x) \\ 35 - 49x &= -320 - 120x \\ 71x &= -355 \\ x &= -5 \end{aligned} \]
Then substitute:
\[ \frac{2x + 3}{x + 9} = \frac{-10 + 3}{-5 + 9} = -\frac{7}{4} \]
Check: with \(x = -5\), \(\frac{5 + 35}{8 - 15} = \frac{40}{-7}\), as given. Once \(x\) is fixed the fraction has only one value, so the other three options cannot be right; a common slip is losing the minus sign on \(\frac{40}{7}\), which gives a different \(x\).
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