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2.3 Solving Multi-Step Equations: Combining like Terms: Simplify the terms with the same variable using arithmetic. Term: A number, a variable or a product.

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Presentation on theme: "2.3 Solving Multi-Step Equations: Combining like Terms: Simplify the terms with the same variable using arithmetic. Term: A number, a variable or a product."— Presentation transcript:

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

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 – m 5 = 5m – m 5 = 5m + 2m – 23 5 = 7m – 23 Add like terms Inverse of subtraction 28 = 7m __ ___ 7 7 Inverse of multiplication m = 4 Dont forget to check!! Same variable

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 $ x One time charge of $ The family paid = $1132 Insurance for each ticket is $19 19x 167x + 19x + 16 = 1132

6 186x + 16 = 1132 Like terms 186x = Inverse of Add 186x = 1116Like 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 11x – 6x – 8 = 22 5x – 8 = 22 Add like terms + 8 = +8 Inverse of subtraction 5x = 30 __ ___ 5 5 Inverse of multiplication x = 6Dont forget to check!! Same variable Given

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 – 16x + 8 = 36 Multiplication – 8 – 8 Inverse of addition _____ ____ – 16 – 16 Inverse of multiplication x = - 28/16 - 7/4 Dont forget to check!! Distributive – 8 – 16x = 28

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

11 Solution: 18 = 3(2x – 6) 18 = 3(2x) + 3(-6) Multiplication Inverse of subtraction __ ___ 6 6 Inverse of multiplication x = 6 Dont forget to check!! Distributive 3 36 = 6x 18 = 6x – 18 Given

12 Solving equations with fractions: Multiplication Same Denominator Common Denominator Subtraction

13 Inverse of Multiplication Inverse of division ___ ___ 5 5 Dont forget to check!!

14 YOU TRY IT:

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

16 Solution: 23b = 60Opposite of multiplying by 23 Dont forget to Check! Multiply by 20 both sides

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

18 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.

19 VIDEOS: Multi-Step Equations Multi-Step nal-expressions/solving-rational-equations/v/ex-1- multi-step-equation g-linear-equations-and- inequalities/complicated_equations/v/ex-2-multi- step-equation

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


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