Discussion
If \(\frac{7x-1}{4}-\frac{1}{3}\left(2x-\frac{1-x}{2}\right)=\frac{10}{3}\), then what is the value of \(\frac{11x+21}{2}\)?
Answer: C
The value is 31.
Simplify the bracket first, then clear the fractions by multiplying by 12.
\[ \begin{aligned} 2x - \frac{1 - x}{2} &= \frac{5x - 1}{2} \\ \frac{7x - 1}{4} - \frac{5x - 1}{6} &= \frac{10}{3} \\ 3(7x - 1) - 2(5x - 1) &= 40 \\ 11x - 1 &= 40 \\ 11x &= 41 \end{aligned} \]
The expression asked for needs only \(11x\), so there is no need to find \(x\) itself:
\[ \frac{11x + 21}{2} = \frac{41 + 21}{2} = 31 \]
The usual slip is in the sign of the last term: \(-2(5x - 1) = -10x + 2\), not \(-10x - 2\). Getting it wrong gives \(11x = 45\) and a value of 33, which is not offered.
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