Solving Linear Equations for a Specified Variable

Equations, Inequalities, and Problem Solving

Solving Linear Equations for a Specified Variable

In intermediate algebra, it is often necessary to solve equations for a particular variable. This process is called solving for a specified variable or literal equations. The goal is to isolate the desired variable on one side of the equation using algebraic operations.

• Addition Property of Equality: You can add the same value to both sides of an equation without changing its equality.

• Division Property of Equality: You can divide both sides of an equation by the same nonzero value to maintain equality.

Example: Solve the equation $Z = AB - 4$ for $A$.

1. Isolate the term containing the specified variable: Add 4 to both sides to move the constant to the left side. $Z + 4 = AB - 4 + 4$ $Z + 4 = AB$

2. Solve for the variable: Divide both sides by $B$ to isolate $A$. $\dfrac{Z + 4}{B} = A$

Final Solution:

$A = \dfrac{Z + 4}{B}$

Application: This technique is useful in science and engineering, where formulas often need to be rearranged to solve for a particular variable.