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2.3 Solving Multi-Step Equations:

Term: A number, a variable or a product or quotient of numbers and variables that is added or subtracted in an algebraic expression. 2.3 Solving Multi-Step Equations:. Combining like Terms: Simplify the terms with the same variable using arithmetic. GOAL: .

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2.3 Solving Multi-Step Equations:

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  1. Term: A number, a variable or a product or quotient of numbers and variables that is added or subtracted in an algebraic expression. 2.3 Solving Multi-Step Equations: Combining like Terms: Simplify the terms with the same variable using arithmetic.

  2. GOAL:

  3. We solve multi-step equations by forming a series of simpler equations by first using combination of like terms: Ex: What is the solution of 5 = 5m – 23 + 2m 5 = 5m – 23 + 2m Same variable 5 = 5m + 2m – 23 5 = 7m – 23 Add like terms +23 + 23 Inverse of subtraction 28 = 7m __ ___ 7 7 Inverse of multiplication Don’t forget to check!! m = 4

  4. REAL-WORLD: A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket for $19 per ticket. The web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy?

  5. SOLUTION: Using the given info we have: Each ticket (x) costs $167  167x Insurance for each ticket is $19  19x One time charge of $16  +16 The family paid  = $1132  167x + 19x + 16 = 1132

  6.  167x + 19x + 16 = 1132 Like terms 186x + 16 = 1132 Inverse of Add 186x + 16-16 = 1132-16 186x = 1116 Like terms 186x /186 = 1116 /186 Inverse of mult. x = 6 Tickets

  7. YOU TRY IT: What is the solution of 11x – 8 – 6x = 22

  8. Solution: 11x – 8 – 6x = 22 Given 11x – 6x – 8 = 22 Same variable Add like terms 5x – 8 = 22 + 8 = +8 Inverse of subtraction 5x = 30 Inverse of multiplication __ ___ 5 5 x = 6 Don’t forget to check!!

  9. Solving equations with Distributive Property: Ex: What is the solution of – 8 (2x -1)= 36 – 8 (2x -1)= 36 – 8(2x) – 8(-1)= 36 Distributive – 8 – 16x + 8 = 36 Multiplication – 8 – 8 Inverse of addition – 16x = 28 _____ ____ – 16 – 16 Inverse of multiplication x = - 28/16  - 7/4 Don’t forget to check!!

  10. YOU TRY IT: What is the solution of 18 = 3(2x – 6 )?

  11. Solution: Given 18 = 3(2x – 6) 18= 3(2x) + 3(-6) Distributive 3 18= 6x – 18 Multiplication +18 +18 Inverse of subtraction 36 = 6x __ ___ 6 6 Inverse of multiplication x = 6 Don’t forget to check!!

  12. Solving equations with fractions: Ex: What is the solution of - = 10? - = 10 Common Denominator - = 10 Multiplication Same Denominator = 10 = 10 Subtraction

  13. 12 = 10 12 Inverse of division 5 = 120 5 = 120 ___ ___ 5 5 Inverse of Multiplication = 24 Don’t forget to check!! Check: - = 10  3(6) - 8  18 - 8  10 = 10

  14. YOU TRY IT: What is the solution of + = 3?

  15. Solution: + = 3 Common Denominator + = 3 = 3 Add the numerators = 3 Opposite of dividing by 20

  16. Solution: (20) = 3(20) Multiply by 20 both sides 23b = 60 Opposite of multiplying by 23 b = Don’t forget to Check!

  17. Check: + = 3 + = 3 b = Plug in our answer + = 3 We never divide fractions,We keep, change and flip! = 3 ) +

  18. Cross Cancel: Divide a numerator with a denominator (only on the same fraction) 24 45 ) + + Add the numerators: since our denominators are the same. Since 69/23 = 3 and 3 =3 we have gotten the right answer.

  19. VIDEOS: Multi-Step Equations Multi-Step http://www.khanacademy.org/math/algebra/rational-expressions/solving-rational-equations/v/ex-1-multi-step-equation http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/complicated_equations/v/ex-2-multi-step-equation

  20. Pages: 97-100 Problems: As many as you need to master the concepts. Class Work:

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