Discussion
If |9y−6| =3, then y2 −4y/3 is _______.
Answer: C
The value is \(-\frac{1}{3}\).
\(|9y - 6| = 3\) gives \(9y - 6 = 3\) or \(9y - 6 = -3\), so \(y = 1\) or \(y = \frac{1}{3}\). Evaluate \(y^{2} - \frac{4y}{3}\) for each:
\[ \begin{aligned} y = 1 &: 1 - \tfrac{4}{3} = -\tfrac{1}{3} \\ y = \tfrac{1}{3} &: \tfrac{1}{9} - \tfrac{4}{9} = -\tfrac{1}{3} \end{aligned} \]
Both roots give the same value, so the expression is well defined and equals \(-\frac{1}{3}\). The value \(+\frac{1}{3}\) is a sign slip, 0 would need \(y = \frac{4}{3}\), and 'undefined' would only apply if the two roots gave different values.
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