Discussion

If 5(3x + 4) − 8(6x + 7) = 9x − 8, then what is the value of \((x^{2} - 2x + 1)\) ?

Answer: D

The value of \(x^{2} - 2x + 1\) is \(\frac{25}{9}\).

Solve the equation first:

\[ \begin{aligned} 15x + 20 - 48x - 56 &= 9x - 8 \\ -33x - 36 &= 9x - 8 \\ -42x &= 28 \\ x &= -\tfrac{2}{3} \end{aligned} \]

Then \(x^{2} - 2x + 1 = (x - 1)^{2} = \left(-\tfrac{5}{3}\right)^{2} = \tfrac{25}{9}\).

\(\tfrac{2}{3}\) is the magnitude of x itself, \(\tfrac{4}{9}\) is \(x^{2}\), and \(\tfrac{5}{3}\) is \(|x - 1|\) before squaring.

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