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.

GOAL:

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 + 2m5 = 5m – 23 + 2m5 = 5m + 2m – 23 5 = 7m – 23 Add like terms

+23 + 23 Inverse of subtraction28 = 7m __ ___

7 7Inverse of multiplication

m = 4 Don’t forget to check!!

Same variable

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 167x

One time charge of $16 +16

The family paid = $1132

Insurance for each ticket is $19 19x

167x + 19x + 16 = 1132

167x + 19x + 16 = 1132

186x + 16 = 1132 Like terms

186x + 16-16 = 1132-16 Inverse of Add

186x = 1116 Like terms

186x /186 = 1116 /186 Inverse of mult.

x = 6 Tickets

YOU TRY IT:

What is the solution of

11x – 8 – 6x = 22

Solution:11x – 8 – 6x = 22

11x – 6x – 8 = 22

5x – 8 = 22 Add like terms+ 8 = +8 Inverse of subtraction 5x = 30 __ ___

5 5Inverse of multiplication

x = 6 Don’t forget to check!!

Same variableGiven

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 Don’t forget to check!!

Distributive – 8

– 16x = 28

YOU TRY IT:

What is the solution of

18 = 3(2x – 6 )?

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

Multiplication +18 +18 Inverse of subtraction

__ ___ 6 6

Inverse of multiplication

x = 6 Don’t forget to check!!

Distributive 3

36 = 6x

18 = 6x – 18

Given

Solving equations with fractions:

Ex: What is the solution of - = 10?

Multiplication

Same Denominator

Common Denominator - = 10

- = 10

= 10

= 10 Subtraction

Inverse of Multiplication

12 = 10 12 Inverse of division

5 = 120

5 = 120 ___ ___ 5 5 = 24 Don’t forget to check!!

Check: - = 10 3(6) - 8 18 - 8 10 = 10

YOU TRY IT:

What is the solution of

+ = 3?

Solution:

Add the numerators

Common Denominator + = 3

+ = 3

= 3

= 3 Opposite of dividing by 20

Solution:

(20) = 3(20)

23b = 60 Opposite of multiplying by 23

b = Don’t forget to Check!

Multiply by 20 both sides

Check: + = 3

We never divide fractions,We keep, change and flip!

Plug in our answer + = 3

+ = 3

= 3

b =

) +

) + 24

+

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

𝟐𝟒+𝟒𝟓𝟐𝟑

= 3

Add the numerators: since our denominators are the same.

𝟔𝟗𝟐𝟑

= 3Since 69/23 = 3 and 3 =3 we have gotten the right answer.

VIDEOS: Multi-Step Equations

Multi-Stephttp://www.khanacademy.org/math/algebra/rational-expressions/solving-rational-equations/v/ex-1-multi-step-equationhttp://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/complicated_equations/v/ex-2-multi-step-equation

Class Work:

Pages: 97-100

Problems: As many as you need to master

the concepts.