Solve each equation for the indicated variable. (Objective...

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Key Concepts

Algebraic Manipulation

Algebraic manipulation involves applying operations such as addition, subtraction, multiplication, and division to both sides of an equation to simplify the expression and ultimately isolate the variable. This concept is fundamental to solving equations and transforming them into a suitable form for further analysis.

Isolation of the Variable

Isolation of the variable is the process of rearranging an equation so that the variable of interest appears on one side of the equation alone. This is achieved by systematically undoing the operations that are obstructing the variable, thereby expressing it in terms of the other quantities in the equation.

Division Property of Equality

The division property of equality states that if both sides of an equation are divided by the same non-zero number, the equality is maintained. This property is essential when a variable is multiplied by a constant, as it allows the solver to remove the constant and isolate the variable effectively.

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