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Algebra 3.4 Notes Name:_______________________________________ Mitchell/Grice 3.4: Solving Equations with Variables on Both Sides Objective: o Solve equations with variables on both sides of the equal sign. (1) SIMPLIFY BOTH SIDES OF THE EQUATION, IF NECESSARY. (Distributive Property, Combine Like Terms, Standard Form) (2) GET THE VARIABLE TO ONE SIDE OF THE EQUATION USING INVERSE OPERATIONS. (Get the x’s to one side) (3) USE INVERSE OPERATIONS TO ISOLATE THE VARIABLE. (Get x by itself) o Solve each of the following equations for x. 1) 2x −12 = 5x 2) −3x + 35 = 2x 3) 3x − 7 = 5x + 9 4) x − 8 = 4x −14 5) 2x − 6 = −3x + 14 6) −3x − 8 = 5x − 32 7) −4x + 7 = −2x + 15 8) −5x − 4 = −6x −11 o Solve each of the following equations for x. 1) 5x + 3 − 2x = x −17 2) −2x + 9 = 5x + 1 − 9x 3) 4x − 5 − x = 4x −12 4) 7x −1 = 3x −10 − 5x 5) 2x − 3x + 7 = 3x + 15 6) −6x + 7 = 9 − 5x −13 7) 7 − 9x − 3 = −3x −14 8) 2x − 9 = 3x + 15 − 5x o All of the equations that we have been solving have had one solution. It is possible for an equation to have one solution, solution no solutions, solutions or many solutions. solutions o NO SOLUTIONS: __________________________________________________________________________ __________________________________________________________________________ EX: o 3x − 7 = 3x + 11 MANY SOLUTIONS: ________________________________________________________________________ ________________________________________________________________________ EX: o 2x − 5 = 2x − 5 Determine if the following equations have one solution, solution no solutions, solutions or many solutions solutions. utions 1) 2x − 3 = 5x − 7 − 3x 2) 7x + 5 − 2x = 5x + 5 3) x − 4 = 4x + 7 − 5x 4) 4x + 9 = −2x + 5 + 6x 5) 3x − 6 − 5x = −2x − 6 6) −4x + 7 = 5x −1 − x