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Solving Two Step Equations

Algebra. Solving Two Step Equations. 3a + 5 = 11. -3n + 16 = - 2. Students will solve two-step equations using inverse operations. -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: -2 – 3 = ?.

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Solving Two Step Equations

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

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

  3. 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)

  4. 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

  5. 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 

  6. Example 2 11n + 1 = 67 – 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 

  7. Example 3 -2y + 4 = 8 – 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 

  8. Example 4 5x – 2 = 3 +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 

  9. Example 5 x 5 – 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

  10. Word Problem #1 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? = 28 Let T = the price of each T-shirt. + 16 3T – 16 – 16Subtraction Property of Equations 3T = 12 3 3 Division Property of Equations T = 4 Each T-shirt cost $4 .

  11. 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? 73 Let F = the price of each decorated flower. + 28 = 9F – 28 – 28Subtraction Property of Equations 9F = 45 9 9 Division Property of Equations F = 5 The decorated flowers were $5.00 each.

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

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

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