1-3: Solving Equations Algebra II

Verbal to Algebraic Expression Write an algebraic expression to represent each verbal expression ◦7 less than a number ◦Three times the square of a number ◦The cube of a number increased by 4 times the same number ◦Twice the sum of a number and 5

Verbal to Algebraic Expression Write an algebraic expression to represent each verbal expression ◦7 less than a number n - 7 ◦Three times the square of a number ◦The cube of a number increased by 4 times the same number ◦Twice the sum of a number and 5

Verbal to Algebraic Expression Write an algebraic expression to represent each verbal expression ◦7 less than a number n - 7 ◦Three times the square of a number 3n 2 ◦The cube of a number increased by 4 times the same number ◦Twice the sum of a number and 5

Verbal to Algebraic Expression Write an algebraic expression to represent each verbal expression ◦7 less than a number n - 7 ◦Three times the square of a number 3n 2 ◦The cube of a number increased by 4 times the same number n 3 + 4n ◦Twice the sum of a number and 5

Verbal to Algebraic Expression Write an algebraic expression to represent each verbal expression ◦7 less than a number n - 7 ◦Three times the square of a number 3n 2 ◦The cube of a number increased by 4 times the same number n 3 + 4n ◦Twice the sum of a number and 5 2(n+5)

Algebraic to Verbal Sentence Write a verbal sentence to represent each algebraic equation: 10 = 12 – 2 n + (-8) = -9 n = n 2 6

Algebraic to Verbal Sentence Write a verbal sentence to represent each algebraic equation: 10 = 12 – 2 ten is equal to 12 minus 2 n + (-8) = -9 n = n 2 6

Algebraic to Verbal Sentence Write a verbal sentence to represent each algebraic equation: 10 = 12 – 2 ten is equal to 12 minus 2 n + (-8) = -9 the sum of a number and -8 is -9 n = n 2 6

Algebraic to Verbal Sentence Write a verbal sentence to represent each algebraic equation: 10 = 12 – 2 ten is equal to 12 minus 2 n + (-8) = -9 the sum of a number and -8 is -9 n = n 2 6 a number divided by 6 is equal to that number squared

Properties of Equality PropertySymbolsExamples ReflexiveFor any real number a, a = a -7 + n = -7 + n SymmetricFor all real numbers a and b, if a = b, then b = a If 3 = 5x – 6, then 5x – 6 = 3 TransitiveFor all real numbers a, b, and c, if a = b, and b = c, then a = c If 2x+1=7 and 7=5x-8, then 2x+1=5x-8 SubstitutionIf a = b, then a may be replaced by b and b may be replaced by a If (4+5)m=18, then 9m=18

Identify the Property of Equality If 3m = 5n and 5n = 10p, then 3m=10p If -11a + 2 = -3a, then -3a = -11a + 2

Identify the Property of Equality If 3m = 5n and 5n = 10p, then 3m=10p Transitive Property of Equality If -11a + 2 = -3a, then -3a = -11a + 2

Identify the Property of Equality If 3m = 5n and 5n = 10p, then 3m=10p Transitive Property of Equality If -11a + 2 = -3a, then -3a = -11a + 2 Symmetric Property of Equality

More Properties of Equality Addition and Subtraction Properties of Equality ◦If a=b, then a+c=b+c and a-c=b-c ◦if two items are equal and you add or subtract the same number to both, they remain equal ◦Example: If x-4=5, then x – = If n+3=11, then n+3-3=11-3 Multiplication and Division Properties of Equality ◦If a=b, then ac=bc, and if c≠0, a = b c c ◦If two items are equal and you multiply or divide them both by the same number they will remain equal

Solve One-Step Equations 1) a = 76 2) 3d = 18 5

Solve a Multi-Step Equation 1) 2(2x + 3) – 3(4x – 5) = 22 2) 53 = 3(y-2) – 2(3y-1)

Solve for a Variable Solve for l S = Πrl + Πr 2

Write an Equation Write an equation, then solve. Let c represent the cost of each door. Josh and Pam have bought an older home that needs some repair. After budgeting a total of $1685 for home improvements, they started by spending $425 on small improvements. They would like to replace six interior doors next. What is the maximum amount they can afford to spend on each door?

Homework 19, 20, 29, even 57-58, 63