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Concept

# Equivalent Equation

Equivalent equations are produced when the Properties of Equality have been applied to an equation. By performing the same operation on both sides of an equation, the form of the equation changes, but its value remains the same – thus, the equations are equivalent. $\begin{gathered} 2x-1=5\\ \Updownarrow\\ 2x-1\ {\color{#0000FF}{+\ 1}}\ =5\ {\color{#0000FF}{+\ 1}}\\ \Updownarrow\\ 2x=6 \end{gathered}$ In the given equation, $1$ is being subtracted from $2x;$ since the inverse operation of subtraction is addition, applying the Addition Property of Equality would simplify the equation. As a result, the equivalent equation $2x=6$ is formed.