1. You have 128 ounces of milk and drink 16 ounces per day. Write an algebraic expression modeling the amount of milk you have

2. Evaluate for a = - 2 and b = 3

Warm – up #3

Warm – up #3 Solutions

1. 128 – 16x x = # of days

2. =

= = = = = = 24

Lesson 1 – 4 Solving Equations

Algebra II

To solve equations

To solve problems by writing equations

Learning Objective

Reflexive Property◦a = a◦5 = 5

Symmetric Property◦If a = b, then b = a◦If = 0.5, then 0.5 =

Transitive Property◦If a = b, and b = c, then a = c◦If x = 3, and 3 = y, then x = y

Properties of Equality

Substitution

◦If a = b, then you can replace a with b, and vice versa

◦If x = y and 9 + x = 15, then 9 + y = 15

Properties of Equality

Addition Property◦If a = b, then a + c = b + c◦If x = 12, then x + 3 = 12 + 3

Subtraction Property◦If a = b, then a – c = b – c◦If x = 12, then x – 3 = 12 – 3

Properties of Equality

Multiplication Property◦If a = b, then a c = b c◦If x = 12, then x 3 = 12 3

Division Property◦If a = b, then a c = b c (c ◦If x = 12, then x 3 = 12 3

Properties of Equality

Equation – a statement that two expressions are equal

Solution(s) of the equation – All values of the variable that make the equation true

Inverse operations – operations that “undo” each other. + & -

1. x + 4 = –12 – 4 = – 4 x = –16

2. 12x = 1812 12x =

Solve a One-Step Equation

3. -27 + 6y = 3(y – 3)-27 + 6y = 3y – 9 - 3y - 3y -27 + 3y = –9 +27 + 27

3y = 183 3y = 6

Solve a Multi-Step Equation

4. 3(2x – 1) – 2(3x + 4) = 11x6x – 3 – 6x – 8 = 11x - 11 = 11x

11 11 x = - 1

Solve a Multi-Step Equation

5. 11 + 3x – 7 = 6x + 5 – 3x4 + 3x = 3x + 5 - 3x -3x 4 = 5NEVER TRUE!!!

No Solution!!

Solve a Multi-Step Equation

6. 6x + 5 – 2x = 4 + 4x + 14x + 5 = 4x + 5 - 5 - 5 4x = 4x

-4x - 4x0 = 0

ALWAYS TRUE!!!Infinite Solution!!

Solve a Multi-Step Equation

7. 7x + 6 – 4x = 12 + 3x - 83x + 6 = 3x + 4-3x -3x 6 = 4

NEVER TRUE!!!

No Solution!!

Solve a Multi-Step Equation

8. 2x + 3(x – 4) = 2(2x – 6) + x2x + 3x – 12 = 4x – 12 + x 5x – 12 = 5x – 12

+ 12 + 12 5x = 5x

-5x - 5x0 = 0

ALWAYS TRUE!!! Infinite Solution!!

Solve a Multi-Step Equation

Literal Equation – an equation that uses at least two different letters as variables.

◦Can solve for any one of its variables.

◦You solve for a variable “in terms of” the other variables

9. What is F in terms of C?] +32 + 32

Solve a Literal Equation

Solve for x.10. x + 3 = 4y – 2w - 3 - 3x = 4y – 2w - 3

Solve a Literal Equation

Solve for x.11. (2x – a)a – c = 2mx - am + am + ama – c + am = 2mx 2m 2m

Solve a Literal Equation

12. A rectangle has a perimeter of 200 meters. The length is three times the width.

What are the dimensions of the rectangle?

Using an equation to solve a problem

x

3x

Wid

th

Length

P = 2(length) + 2(width)200 = 2(3x) + 2(x)200 = 6x + 2x200 = 8x 8 8

x = 25

Width = 25 m

Length = 75 m

A city park has a pool. You can pay a daily entrance fee of $3 or purchase a membership for the 12-week summer season for $82 and pay only $1 per day to swim. How many days would you have to swim to make the membership worthwhile?

Ticket Out the Door

Assignment:

Pg. 30 #11 – 25 odd, 30 – 40 all