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:

Step1: Apply Zero-Product Property

If \(ab = 0\), then \(a = 0\) or \(b = 0\). So for \((2x - 5)(3x - 1)=0\), we set \(2x - 5 = 0\) or \(3x - 1 = 0\).

Step2: Solve \(2x - 5 = 0\)

Add 5 to both sides: \(2x=5\). Divide by 2: \(x = \frac{5}{2}\).

Step3: Solve \(3x - 1 = 0\)

Add 1 to both sides: \(3x = 1\). Divide by 3: \(x=\frac{1}{3}\).

Answer:

\(x=\frac{5}{2}\) or \(x=\frac{1}{3}\) (corresponding to the option: \(x=\frac{5}{2}\) or \(x=\frac{1}{3}\))