Discussion
If \(\frac{5x - 7}{3} + 2 = \frac{4x - 3}{4} + 4x\), then the value of \((8x + 5)\) is
Answer: A
The value of \((8x + 5)\) is 6.
Clear the fractions by multiplying both sides by 12, the LCM of 3 and 4.
\[ \begin{aligned} 4(5x - 7) + 24 &= 3(4x - 3) + 48x \\ 20x - 4 &= 60x - 9 \\ 5 &= 40x, \quad x = \tfrac{1}{8} \end{aligned} \]
\[ 8x + 5 = 1 + 5 = 6 \]
Check: with \(x = \frac{1}{8}\) both sides equal \(-\frac{1}{8}\). The usual error is forgetting to multiply the lone terms (2 and \(4x\)) by 12, which gives a wrong x and hence a wrong value of \(8x + 5\).
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