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Why? - Mainly to help in solving equations.
You often need the additive property of equality. It says if a=b then a+c=b+c.This alone may be enough to solve many equations. Sometimes you need to multiply or divide both sides. This is the multiplicative property of equality.
It is important to know several techniques for solving equations and inequalities because one may work better than another in a particular situation.
If x=y then x+z=y+z or If x=y and a=b then x+a=y+b The formal name for the property of equality that allows one to add the same quantity to both sides of an equation. This, along with the multiplicative property of equality, is one of the most commonly used properties for solving equations.
An equality and equation are essentially the same thing. The equality between two expressions is represented by an equation (and conversely).