An inventory analyst uses the equation -4(a - 3) - 7 = 25 to model the weekly depletion of a specific SKU. To find the value of 'a', the analyst must follow a specific sequence of algebraic steps. Arrange these steps in the correct order.

A production manager is using the equation -4(a - 3) - 7 = 25 to model supply chain delays. According to the standard procedure for simplifying an equation before isolating the variable, which mathematical step should be performed first on the left side?

A project supervisor is using the equation $-4(a - 3) - 7 = 25$ to determine a resource allocation variable 'a'. True or False: When simplifying the left side of the equation, multiplying the factor $-4$ by the term $-3$ results in $-12$.

A project budget analyst is documenting the algebraic steps used to solve the cost-adjustment equation -4(a - 3) - 7 = 25. Match each specific transformation of the equation to the mathematical property or action that justifies it.

A facility manager is using the equation $-4(a - 3) - 7 = 25$ to determine an energy-efficiency variable $a$. After the manager correctly distributes the $-4$ and combines the constant terms on the left side, the equation simplifies to $-4a +$ ____ $= 25$.

Finalizing a Logistics Formula

Verifying Solutions through Substitution

Documenting Equation Simplification Protocols

A financial analyst is documenting the algebraic steps used to simplify the cost-adjustment formula $-4(a - 3) - 7 = 25$. In the first step, the analyst distributes the $-4$ across the parentheses, resulting in $-4a + 12 - 7 = 25$. Which fundamental mathematical rule justifies why the constant term becomes positive $12$?

A quality control analyst is documenting the standard procedure for solving the resource allocation formula $-4(a - 3) - 7 = 25$. After the formula has been simplified to the step $-4a = 20$, the analyst must justify the final calculation. According to the provided procedure, why are both sides of the equation divided by $-4$?