Subtraction Property of Equality

Subtracting the same number from both sides of an equation results in an equivalent equation. Let a, b, and c be real numbers.

If a = b, then a - c = b - c.

The Subtraction Property of Equality is an axiom, so it does not need a proof. This property is one of the Properties of Equality that can be used when solving equations. Consider an example. x+2=7 By subtracting 2 from both sides of the equation, the variable x can be isolated and the solution to the equation can be found.

x+2=7

SubEqn

LHS- 2=RHS- 2

x+2 - 2=7 - 2

Simplify left-hand side

x + 2 - 2=7-2

SubTerms

Subtract terms

x=5

Note that the Subtraction Property of Equality also holds true if a, b, and c are complex numbers.

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