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

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