Happy Tuesday

Ready for a great 4 day week

Warm – up #3

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 Solutions

1. 128 – 16x x = # of days

2.

=

=

=

=

=

= = 24

Lesson 1 – 4 Solving EquationsAlgebra II

Learning Objective To solve equations

To solve problems by writing equations

Properties of Equality 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

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. + & -

Solve a One-Step Equation

1. x + 4 = –12

– 4 = – 4

x = –16

2. 12x = 18

12 12

x =

Solve a Multi-Step Equation

3. -27 + 6y = 3(y – 3)

-27 + 6y = 3y – 9

- 3y - 3y

-27 + 3y = –9

+27 + 27

3y = 18

3 3

y = 6

Solve a Multi-Step Equation

4. 3(2x – 1) – 2(3x + 4) = 11x

6x – 3 – 6x – 8 = 11x

- 11 = 11x

11 11

x = - 1

Solve a Multi-Step Equation

5. 11 + 3x – 7 = 6x + 5 – 3x

4 + 3x = 3x + 5

- 3x -3x

4 = 5

NEVER TRUE!!!

No Solution!!

Solve a Multi-Step Equation

6. 6x + 5 – 2x = 4 + 4x + 1

4x + 5 = 4x + 5

- 5 - 5

4x = 4x

-4x - 4x

0 = 0

ALWAYS TRUE!!!

Infinite Solution!!

Solve a Multi-Step Equation

7. 7x + 6 – 4x = 12 + 3x - 8

3x + 6 = 3x + 4

-3x -3x

6 = 4

NEVER TRUE!!!

No Solution!!

Solve a Multi-Step Equation

8. 2x + 3(x – 4) = 2(2x – 6) + x

2x + 3x – 12 = 4x – 12 + x

5x – 12 = 5x – 12

+ 12 + 12

5x = 5x

-5x - 5x

0 = 0

ALWAYS TRUE!!!

Infinite Solution!!

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

Solve a Literal Equation9.

What is F in terms of C?

]

+32 + 32

Solve a Literal EquationSolve for x.

10.

x + 3 = 4y – 2w

- 3 - 3

x = 4y – 2w - 3

Solve a Literal EquationSolve for x.

11.

(2x – a)

a – c = 2mx - am

+ am + am

a – c + am = 2mx

2m 2m

Using an equation to solve a problem

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

What are the dimensions of the rectangle?

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

Assignment:

Pg. 30 #11-25 odd, 33-40 ALL