1-3 ALGEBRAIC EXPRESSIONSEvaluate and simplify algebraic expressions by substituting and using order of operations.

How to…• You will need to translate words into mathematical

operations. • What are some words or phrases for:

• Addition Subtraction

• Multiplication Division

Practice

• Ex: The product of 9 and b• 9b

• 26 less than 12 (**when you see “less than” notice that the first number goes last)• 12 - 26

You try:• The quotient of 6 and 3

• 6 more than twice the points

• Two times the sum of a and b

Modeling a Situation• You start with $20 and save $6 each week. What

algebraic expression models the total amount you save?• What do we know?• How can we make an algebraic expression using what we

know?

• 20 + 6w

Evaluate an Algebraic Expression

• Replace variables with values• Use order of operations to simplify• Ex: q + r – 15 if q = 21 and r = 18

• 21 + 18 -15• 39 – 15• 24

Simplifying Expressions• Combine like terms

• Use commutative property• • Combine

• If there is any distributing to be done… distribute FIRST!

1-4 SOLVING EQUATIONSSolve problems by writing equations.

Equation • An equation is a statement that two expressions are

equal.• Equations have an equal sign, expressions do not.

Properties of Equality• Reflexive: a = a

• Ex: 5 = 5

• Symmetric: If a = b, then b = a• Ex: If ½ = 0.5, then 0.5 = ½

• Transitive: If a = b and b = c, then a = c• Ex: If 2.5 = and , then

• Substitution: If a = b, then you can replace a with b and vice versa.• Ex: If a = b and 9 + a = 15, then 9 + b = 15

Solving• A solution of an equation is a value that makes the

equation true.• To find a solution, use inverse operations to “undo” the

equation.• Must be done to BOTH sides of the equation.

• If there is distributing to do, do it first.• Next, undo any addition or subtraction.• Last, undo multiplication or division.• Ex:

• distribute• add 27• subtract 3y• divide by 3

No Solution or Identities• Equations have no solution if all variables cancel and the

statement is false.• Ex: 4 = 5 (there are no variables and we know that 4 5)

• Equations have infinitely many solutions or are identities if all variables cancel and the statement is true.• Ex: 0 = 0 (notice the answer is not zero. We know that it is true that

0 = 0 so the equation is an identity)

Literal Equations• An equation that uses at least 2 different variables.• You solve for a variable “in terms of” the other variables.

• Isolate one of the variables and get all others to the opposite side of the equal sign.

• You Try:• The equation relates temperatures in degrees Fahrenheit

F and degrees Celsius C. What is F in terms of C?• multiply by the reciprocal • add 32

Assignment• Odds p.22 #13-21

p.30 #21-33