1 3 Solving Equations Algebra II Verbal to
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 3 n 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 3 n 2 ◦ The cube of a number increased by 4 times the same number n 3 + 4 n ◦ 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 3 n 2 ◦ The cube of a number increased by 4 times the same number n 3 + 4 n ◦ 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 6 = n 2
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 Property Symbols Examples Reflexive For any real number a, a=a -7 + n = -7 + n Symmetric For all real numbers a and b, if a = b, then b = a If 3 = 5 x – 6, then 5 x – 6 = 3 Transitive For all real numbers a, b, and c, if a = b, and b = c, then a = c If 2 x+1=7 and 7=5 x-8, then 2 x+1=5 x-8 Substitution If a = b, then a may be replaced by b and b may be replaced by a If (4+5)m=18, then 9 m=18
Identify the Property of Equality �If 3 m = 5 n and 5 n = 10 p, then 3 m=10 p �If -11 a + 2 = -3 a, then -3 a = -11 a + 2
Identify the Property of Equality �If 3 m = 5 n and 5 n = 10 p, then 3 m=10 p Transitive Property of Equality �If -11 a + 2 = -3 a, then -3 a = -11 a + 2
Identify the Property of Equality �If 3 m = 5 n and 5 n = 10 p, then 3 m=10 p Transitive Property of Equality �If -11 a + 2 = -3 a, then -3 a = -11 a + 2 Symmetric Property of Equality
More Properties of Equality � Addition and Subtraction Properties ◦ If a=b, then a+c=b+c and a-c=b-c of Equality ◦ 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 – 4 + 4 = 5 + 4 If n+3=11, then n+3 -3=11 -3 � Multiplication and Division Properties of Equality ◦ If a=b, then a • c=b • c, 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 + 4. 39 = 76 2) 3 d = 18 5
Solve a Multi-Step Equation 1) 2) 2(2 x + 3) – 3(4 x – 5) = 22 53 = 3(y-2) – 2(3 y-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, 30 � 35 -40 � 42 -56 even � 57 -58, 63
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