algebra ii to solve equations to solve problems by writing equations
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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
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. + & -
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
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
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