Question

what are the solutions to the equation \\((2x - 5)(3x - 1) = 0\\)?

\\(x = -\frac{5}{2}\\) or \\(x = -\frac{1}{3}\\)

\\(x = \frac{2}{5}\\) or \\(x = 3\\)

\\(x = \frac{5}{2}\\) or \\(x = \frac{1}{3}\\)

\\(x = 5\\) or \\(x = 1\\)

Explanation:

Apply the zero product property

$$ (2x - 5)(3x - 1) = 0 \implies 2x - 5 = 0 \quad \text{or} \quad 3x - 1 = 0 $$

Solve each linear equation

$$
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$$

State the final solutions

$$ x = \frac{5}{2} \quad \text{or} \quad x = \frac{1}{3} $$

Answer:

• (A) \(x = -\frac{5}{2}\) or \(x = -\frac{1}{3}\)
• (B) \(x = \frac{2}{5}\) or \(x = 3\)
• (C) \(x = \frac{5}{2}\) or \(x = \frac{1}{3}\) (Correct answer)
• (D) \(x = 5\) or \(x = 1\)