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

Word Problem #1 3T + 16 = 28 Let T = the price of each T-shirt. Bobby bought 3 T-shirts at the mall and a pair of pants for $16 at the clothing store. All together he spent $28 for the clothes. How much was each shirt? 3T + 16 = 28 Let T = the price of each T-shirt. – 16 – 16 Subtraction Property of Equations 3T = 12 3 3 Division Property of Equations T = 4 Each T-shirt cost $4 .

The decorated flowers were $5.00 each. Word Problem #2 Diane sold 9 decorated flowers that cost the same amount each plus a dozen roses for $28. All together she sold $73 in flowers. How much was each decorated flower? 9F + 28 = 73 Let F = the price of each decorated flower. – 28 – 28 Subtraction Property of Equations 9F = 45 9 9 Division Property of Equations F = 5 The decorated flowers were $5.00 each.

Solve for x with variables ax + b = y – b – b Subtract b from both sides. ax = y – b Since y and b are not like terms, we cannot combine them. a a y – b a x = Divide both sides of the equation by a. y a b a OR x =

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