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

ORDER OF OPERATIONS• Parentheses • Exponents • Multiply/Divide from left to right• Add/Subtract from left to right

Review

Order of Operations

• Simplify: [9 ÷ (42 - 7)] - 8• Exponents [9 ÷ (16 - 7)] - 8• Parentheses [9 ÷ (9)] - 8• Divide [ 1 ] - 8• Subtract -7

Review

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 constant has no

variablesCoefficient is the

numerical factor of a term

Modeling words with algebraic expressions

Seven fewer than a number yy – 7

two times the sum of a and b2(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

1 3 5 1 3772 4 6 4 6x x x

Solving Equations

• Solve: V = πr2h, for h

• Solve: de - 4f = 5g, for e