A department supervisor notes that 3/4 of the quarterly training budget has been spent, totaling 12,000 dollars. To solve the equation (3/4)x = 12,000 for the total budget (x), what is the reciprocal of 3/4 that should be used to multiply both sides?

A technician is using the equation (3/4)x = 12 to calculate the total capacity of a fuel tank. To isolate the variable x, the technician multiplies both sides by the reciprocal 4/3. According to the inverse property of multiplication, the new coefficient of x will be ____.

A project manager determines that 3/4 of a development phase is complete, representing 12 days of work. To find the total length of the phase (x) using the equation (3/4)x = 12, arrange the following steps in the correct order according to the reciprocal multiplication method described in the course.

A workshop facilitator is demonstrating how to solve the equation (3/4)x = 12 to calculate the total production time (x) for a project. To ensure the steps are recognized correctly, match each component of the solution process with its correct algebraic role or description.

Verifying Algebraic Solutions

To solve the equation $\frac{3}{4}x = 12$ for the total inventory count ($x$) using the reciprocal multiplication method, a logistics coordinator should multiply both sides of the equation by $\frac{4}{3}$.

Warehouse Capacity and the Reciprocal Strategy

Procedural Explanation of the Reciprocal Method

A project manager uses the equation $\frac{3}{4}x = 12$ to determine the total hours ($x$) allocated for a training phase. After solving the equation and finding that $x = 16$, the manager needs to verify the result. Which of the following equations correctly shows the 'check' step by substituting the solution back into the original equation?

A technical documentation writer is explaining the algebraic steps used to calculate a project's completion rate based on the equation $\frac{3}{4}x = 12$. To explain why multiplying the coefficient $\frac{3}{4}$ by its reciprocal $\frac{4}{3}$ results in exactly 1, which mathematical property should be cited?