Algebra II To solve equations To solve problems by writing equations.
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Transcript of Algebra II To solve equations To solve problems by writing equations.
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