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 2x1=5. 2x-1=5. One way to begin solving this equation is by adding 11 to both sides. This yields the following. 2x1=5 2x=6 2x-1=5 \Rightarrow \ 2x=6 2x1=52x-1=5 and 2x=62x=6 are equivalent equations because the same value of xx makes them true. Namely, x=3.x=3.

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