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Algebra 1/2 Section 2.5 Solving Multi-step equations with variables on both sides Monday, September 12th Example 1: Solving Equations with Variable on both sides Step 1: Use the Addition or Subtraction Property of Equality to write an equivalent equation with all the variables on one side x – 6 = –2x + 3 x +2x -6 = –2x +2x + 3 3x – 6 = 3 3x – 6 + 6 = 3 + 6 Step 2:Use the Multiplication or Division Property of Equality to solve. Original Equation Add 2x to both sides Simplify Add 6 to both sides 3x = 9 Simplify 3x = 9 3 3 Divide both sides by 3 to isolate the variable. x=3 Example 2: Solving Equations with grouping symbols. Step 1: Simplify the expression on each side. Use the distributive property as needed. Step 2: Use addition and/or subtraction to get all the variables on one side of the equation and the constant terms on the other side. 4(2r – 8) = 1/7(49r+70) 8r - 32 = 7r + 10 8r - 7r - 32 = 7r - 7r + 10 1r - 32 = 10 Original Equation Distribute Subtract 7r from both sides Simplify Add 32 to both sides Step 3: Use division or multiplication to solve. 1r - 32 + 32 = 10 + 32 1r = 42 Simplify Check: 4(2r – 8) = 1/7(49r+70) when r = 42. 4(2r – 8) = 1/7(49r+70) Example 3: Solving Equations with no solution or identity. New Vocabulary: Identity 2m + 5 = 5(m–7) -3m Original Equation 2m + 5 = 5m–35 -3m Distribute 2m - 2m+ 5 = 2m -2m - 35 5 = -35 This statement is false, There is no solution. An equation that is true for all values of the variables. Subtract 2m from both sides 3(r + 1) - 5 = 3r - 2 Original Equation 3r + 3 - 5 = 3r - 2 Distribute 3r - 2 = 3r - 2 Simplify by combining like terms. Simplify Since the Reflexive expressions on each Property of side of the equation Equality are the same this is an Identity. Solve the equations: a. 14 – 3y = 4y b. 4x – 15 = 17 – 4x Solve the equations: c. 10x – 22 = 29 – 7x d. r – 4 + 6r = 3 + 8r Homework Page 101 (11-43 odd, 49, 50) This is different than your assignment sheet so write it down.