Solving the Equation: (7/2x  1)(3x + 4) = 0
This equation is a product of two factors that equals zero. To solve for x, we can use the Zero Product Property. This property states that if the product of two factors is zero, then at least one of the factors must be zero.
Let's break down the steps:

Set each factor equal to zero:
 (7/2x  1) = 0
 (3x + 4) = 0

Solve each equation for x:

For (7/2x  1) = 0:
 Add 1 to both sides: 7/2x = 1
 Multiply both sides by 2/7: x = 2/7

For (3x + 4) = 0:
 Subtract 4 from both sides: 3x = 4
 Divide both sides by 3: x = 4/3


Therefore, the solutions to the equation (7/2x  1)(3x + 4) = 0 are x = 2/7 and x = 4/3.
In conclusion, we've successfully solved the equation using the Zero Product Property. By setting each factor equal to zero and solving for x, we found two distinct solutions: x = 2/7 and x = 4/3.