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Solving Equations by Adding or Subtracting (3-3) Definition: Inverse operations “undo” each other _______________ and _______________ are inverse operations, because they “undo” each other. Subtraction Property of Equality: If you subtract the same number for each side of an equation, the two sides remain equal Ex. 5=5 Ex. x+2=3 __________= ___________ __________= ___________ _____ = _____ _____ = _____ Addition Property of Equality: If you add the same number for each side of an equation, the two sides remain equal Ex. 5=5 Ex. __________= ___________ _____ = _____ n–2=5 __________= ___________ _____ = _____ Definition: Equivalent Equations have the same solution. When you use the Subtractions Property or Addition Property of Equality, you make equivalent equations. Remember that a SOLUTION is the value of the variable that makes the equation true. x+3=7 The solution is x = _____ To Solve Equations you use the Subtraction Property and Addition Property of Equality to “UNDO” what had been added to or subtracted from x, to find the value of the variable Solve each equation. Check your solution. Ex. x+4=7 _______________ = _____________ (Subtraction Property) _______ = _______ (Solution) 1 Ex. 16 + x = 14 __________ = _____ (Commutative Property) _______________ = _____________ (Subtraction Property) _______ = _______ (Solution) Ex. y – 7 = -25 _______________ = _____________ (Addition Property) _______ = _______ (Solution) Ex. x + 8 = -5 _______________ = _____________ (Subtraction Property) _______ = _______ (Solution) Ex. 16 = y + 20 __________ = _____ (Transitive Property) _______________ = _____________ (Subtraction Property) _______ = _______ (Solution) Ex. y – 49 = -13 _______________ = _____________ (Addition Property) _______ = _______ (Solution) 2