Entry Task Find the next three numbers 101,92,83,74….. Now create your own pattern, see if you can stump me.

1-3 Algebraic Expressions Learning Target: Evaluate and simplify algebraic expressions.

Expressions & Formulas Review Expressions & Formulas ORDER OF OPERATIONS Parentheses Exponents Multiply/Divide from left to right Add/Subtract from left to right

Order of Operations Simplify: [9 ÷ (42 - 7)] - 8 Review Order of Operations Simplify: [9 ÷ (42 - 7)] - 8 Exponents [9 ÷ (16 - 7)] - 8 Parentheses [9 ÷ (9)] - 8 Divide [ 1 ] - 8 Subtract -7

Properties

Algebraic Expressions An expression that is a number, a variable or the product of a number and one or more variables is a term. An algebraic expression is an expression that contains at least one variable. -4ax + 7w - 6 Coefficient is the numerical factor of a term constant has no variables

Modeling words with algebraic expressions Seven fewer than a number y y – 7 two times the sum of a and b 2(a + b)

Modeling a situation Savings You start with $20 and save $6 each week. What algebraic expressions models the total amount you save? relate (write using words), define (assign variables), write (use numbers, operations and variables) 20 + 6w

Algebraic Expressions How do you evaluate expressions? You can evaluate an algebraic expression by replacing each variable with a value and then applying the Order of Operations.

Example: Evaluate a(5a + 2b) if a=3 and b=-2 Substitute the values into the expression. 3[5(3) + 2(-2)] Now apply the Order of Operations: Inside the brackets, perform multiplication and division before addition and subtraction 5(3) = 15 and 2(-2)= -4 3[15 + -4] then 15 + -4 = 11 3[11] = 33

Expressions Evaluate: a[b2(b + a)] if a = 12 and b= 1 Substitute: 12[12(1 + 12)] Parentheses: 12[12(13)] Exponents: 12[1(13)] Parentheses: 12[13] Multiply: 156

Expressions – like terms Like terms have the same variable raised to the same power. 3x2 + 5x2 + 9y3x + 2 – 4y3x

Simplify Algebraic Expressions 1. 7x2 + 3y2 + 2y2 – 4x2 =3x2 + 5y2 2. -(3k + m) + 2(k – 4m) = - k – 9m

Assignment P. 22 #11-43 odds

Solving Equations To solve an equation, find replacements for the variables to make the equation true. Each of these replacements is called a solution of the equation. Equations may have {0, 1, 2 … solutions.

Solving Equations 3(2a + 25) - 2(a - 1) = 78 4(x - 7) = 2x + 12 + 2x

Solving Equations Solve: V = πr2h, for h Solve: de - 4f = 5g, for e