To solve the equation \(\frac{2x}{3x} \cdot \frac{4}{3x} = 0\), we can start simplifying the left side.
Simplify \(\frac{2x}{3x}\): \[ \frac{2x}{3x} = \frac{2}{3} \quad (\text{as long as } x \neq 0) \]
Now substitute it back into the equation: \[ \frac{2}{3} \cdot \frac{4}{3x} = 0 \]
Multiply the fractions: \[ \frac{2 \cdot 4}{3 \cdot 3x} = \frac{8}{9x} \]
Now, the equation is: \[ \frac{8}{9x} = 0 \]
A fraction can only equal zero if its numerator is zero. Since \(8\) is not zero, this means that there are no solutions when \(x \neq 0\).
However, we also note that \(x\) cannot be zero in the original equation because of division by zero (which is undefined).
Therefore, the solution to the equation \(\frac{2x}{3x} \cdot \frac{4}{3x} = 0\) is:
No solution.
