Discussion
If \(\dfrac{7x - 1}{4} - \dfrac{1}{7}\left(2x - \dfrac{1 - x}{2}\right) = 4\), then what is the value of \(\dfrac{5x - 3}{3x - 1}\)?
Answer: B
The value is 3/2.
Simplify the bracket first, then clear the fractions:
\[ \begin{aligned} 2x - \frac{1 - x}{2} &= \frac{5x - 1}{2} \\ \frac{7x - 1}{4} - \frac{5x - 1}{14} &= 4 \\ 7(7x - 1) - 2(5x - 1) &= 112 \\ 39x - 5 &= 112,\ x = 3 \end{aligned} \]
Then
\[ \frac{5x - 3}{3x - 1} = \frac{12}{8} = \frac{3}{2} \]
Check: with x = 3 the left side is 20/4 - (1/7)(6 + 1) = 5 - 1 = 4. Since x is fixed, the expression has only one value, so 1, 7/5 and 11/8 cannot be right.
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