Solving Two Step Equations Students will solve two-step equations using inverse operations. Algebra 3a + 5 = 11 -3n + 16 = - 2 -2x – 8 = 16 2y + ( - 3 ) = - 15

Review One-step Equations m + 9 = 3 f – 3 = -5 - 9 - 9 + 3 + 3 m = -6 f = -2 check: -6 + 9 = ? check: -2 – 3 = ? 3 = 3  -5 = -5  (-5) (-5) 3a = -18 3 3 x = 10 a = -6 Check: Check: 3 (-6) = ? -18 = -18  -2 = -2 

Two-Step Equations It takes two steps to solve an equation that has more than one operation. Use PEMDAS backwards Simplify by using the addition or subtraction property of equality. (use the inverse of addition or subtraction) Simplify further by using the multiplication or division property of equality. (use the inverse of multiplication or division)

2-step Equation w/ Algebra Tiles = x = 1 3x + 2 = 11 + = Subtract 2 from each side of the equation. = Divide into equal groups. = x = 3

 Example 1 2x – 15 = 5 +15 +15 Addition Property of Equality 2x = 20 2 2 Division Property of Equality x = 10 CHECK YOUR WORK: 2 ( 10 ) – 15 = ? 20 – 15 5 = 5 

 Example 2 – 1 – 1 Subtraction Property of Equality 11n = 66 11 11 Division Property of Equality n = 6 CHECK YOUR WORK: 11 ( 6 ) + 1 = ? 66 + 1 67 = 67 

 Example 3 – 4 – 4 Subtraction Property of Equality -2y = 4 -2 -2 Division Property of Equality y = -2 CHECK YOUR WORK: -2 (-2 ) + 4 = ? 4 + 4 8 = 8 

 Example 4 +2 +2 Addition Property of Equality 5x = 5 5 5 Division Property of Equality x = 1 CHECK YOUR WORK: 5 ( 1 ) – 2 = ? 5 – 2 3 = 3 

 Example 5 x 5 – 9 = -2 + 9 + 9 Addition Property of Equation x – 9 = -2 + 9 + 9 Addition Property of Equation x 5 ( 5 ) ( 5 ) Multiplication Property of Equation = 7 Check your answer: x = 35 35 5 – 9 = ? 7 – 9  -2 = -2

Remember, use inverse operations to solve equations. Summary Remember, use inverse operations to solve equations. Work in reverse order of operations.