2 3 Solving MultiStep Equations Term A number

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2. 3 Solving Multi-Step Equations: Term: A number, a variable or a product or

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. Combining like Terms: Simplify the terms with the same variable using arithmetic.

GOAL:

GOAL:

We solve multi-step equations by forming a series of simpler equations by first using

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 = 5 m – 23 + 2 m 5 = 5 m + 2 m – 23 5 = 7 m – 23 + 23 28 = 7 m __ ___ 7 7 m=4 Same variable Add like terms Inverse of subtraction Inverse of multiplication Don’t forget to check!!

REAL-WORLD: A family buys airline tickets online. Each ticket costs $167. The family buys

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?

SOLUTION: Using the given info we have: Each ticket (x) costs $167 167 x

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

 167 x + 19 x + 16 = 1132 186 x + 16

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

YOU TRY IT: What is the solution of 11 x – 8 – 6

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

Solution: 11 x – 8 – 6 x = 22 11 x – 6

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

Solving equations with Distributive Property: Ex: What is the solution of – 8 (2

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

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

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

Solution: 18 = 3(2 x – 6) 18 = 3(2 x) + 3(-6) 18

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

Solving equations with fractions: Common Denominator Multiplication Same Denominator Subtraction

Solving equations with fractions: Common Denominator Multiplication Same Denominator Subtraction

 Inverse of division ___ 5 5 Inverse of Multiplication Don’t forget to check!!

Inverse of division ___ 5 5 Inverse of Multiplication Don’t forget to check!!

YOU TRY IT:

YOU TRY IT:

Solution: Common Denominator Add the numerators Opposite of dividing by 20

Solution: Common Denominator Add the numerators Opposite of dividing by 20

Solution: Multiply by 20 both sides 23 b = 60 Opposite of multiplying by

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

 Plug in our answer We never divide fractions, We keep, change and flip!

Plug in our answer We never divide fractions, We keep, change and flip!

24 45 Cross Cancel: Divide a numerator with a denominator (only on the same

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

VIDEOS: Multi-Step Equations Multi-Step http: //www. khanacademy. org/math/algebra/ratio nal-expressions/solving-rational-equations/v/ex-1 multi-step-equation http: //www. khanacademy. org/math/algebra/solvi

VIDEOS: Multi-Step Equations Multi-Step http: //www. khanacademy. org/math/algebra/ratio nal-expressions/solving-rational-equations/v/ex-1 multi-step-equation http: //www. khanacademy. org/math/algebra/solvi ng-linear-equations-andinequalities/complicated_equations/v/ex-2 -multistep-equation

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

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