Concept

Equivalent Equation

Two equations are called equivalent equations when they have the same solution. When using inverse operations to solve an equation, adding, subtracting, multiplying and dividing both sides of the equation by the same number creates equivalent equations. This is due to the Properties of Equality. Consider the equation $2x-1=5.$ One way to begin solving this equation is by adding $1$ to both sides. This yields the following. $2x-1=5 \Rightarrow \ 2x=6$ $2x-1=5$ and $2x=6$ are equivalent equations because the same value of $x$ makes them true. Namely, $x=3.$